Mangasarian, Olvi L. 1934
Overview
Works:  120 works in 420 publications in 5 languages and 2,931 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree 
Classifications:  T57.8, 519.76 
Publication Timeline
.
Most widely held works by
Olvi L Mangasarian
Nonlinear programming by
Olvi L Mangasarian(
Book
)
80 editions published between 1968 and 2014 in 5 languages and held by 1,143 WorldCat member libraries worldwide
This book is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions
80 editions published between 1968 and 2014 in 5 languages and held by 1,143 WorldCat member libraries worldwide
This book is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions
Nonlinear programming 3 : proceedings of the Special Interest Group on Mathematical Programming symposium by
Olvi L Mangasarian(
Book
)
42 editions published between 1978 and 2014 in 3 languages and held by 403 WorldCat member libraries worldwide
Monotone operators and augmented lagrangian methods in nonlinear programming; The convergence of variable metric methods for nonlinearly constrained optimization calculations; A hybrid method for nonlinear programming; Twophase algorithm for nonlinear constraint problems; Quasinewton methods for equality constrained optimization: equivalence of existing methods and a new implementation; An idealized exact penalty function; Exact penalty algorithms for nonlinear programming; A variable metric method for linearly constrained minimization problems; Solving systems of nonlinear equations by broyden's method with project updates; At the interface of modeling and algorithms research; Modeling combinatorial mathematical programming problems by netforms: an illustrative application; On the comparative evaluation of algorithms for mathematical programming problems
42 editions published between 1978 and 2014 in 3 languages and held by 403 WorldCat member libraries worldwide
Monotone operators and augmented lagrangian methods in nonlinear programming; The convergence of variable metric methods for nonlinearly constrained optimization calculations; A hybrid method for nonlinear programming; Twophase algorithm for nonlinear constraint problems; Quasinewton methods for equality constrained optimization: equivalence of existing methods and a new implementation; An idealized exact penalty function; Exact penalty algorithms for nonlinear programming; A variable metric method for linearly constrained minimization problems; Solving systems of nonlinear equations by broyden's method with project updates; At the interface of modeling and algorithms research; Modeling combinatorial mathematical programming problems by netforms: an illustrative application; On the comparative evaluation of algorithms for mathematical programming problems
Nonlinear programming, 2 : proceedings of the Special Interest Group on Mathematical Programming symposium, conducted by the
Computer Sciences Department at the University of WisconsinMadison, April 1517, 1974 by Symposium on Nonlinear Programming(
Book
)
16 editions published between 1974 and 2014 in English and held by 268 WorldCat member libraries worldwide
16 editions published between 1974 and 2014 in English and held by 268 WorldCat member libraries worldwide
Linear programming with MATLAB by
Michael C Ferris(
Book
)
12 editions published in 2007 in English and held by 245 WorldCat member libraries worldwide
This textbook provides a selfcontained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interiorpoint methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and seniorlevel undergraduate students, firstyear graduate students, and researchers unfamiliar with linear programming
12 editions published in 2007 in English and held by 245 WorldCat member libraries worldwide
This textbook provides a selfcontained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interiorpoint methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and seniorlevel undergraduate students, firstyear graduate students, and researchers unfamiliar with linear programming
Complementarity : applications, algorithms, and extensions by
Michael C Ferris(
Book
)
5 editions published between 2001 and 2011 in English and held by 63 WorldCat member libraries worldwide
"New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis and related theory for mathematical programs with equilibrium constraints is also detailed." "Audience: Researchers and advanced students working in optimization and management sciences."Jacket
5 editions published between 2001 and 2011 in English and held by 63 WorldCat member libraries worldwide
"New algorithmic advances including preprocessing and nonmonotone searches, extensions of computational methods using tools from nonsmooth analysis and related theory for mathematical programs with equilibrium constraints is also detailed." "Audience: Researchers and advanced students working in optimization and management sciences."Jacket
Iterative solution of linear programs by
Olvi L Mangasarian(
Book
)
5 editions published in 1979 in English and held by 62 WorldCat member libraries worldwide
By perturbing a linear program to a quadratic program, it is possible to solve the latter in its dual variable space by iterative techniques such as successive overrelaxation (SOR) methods. This solution provides a solution to the original linear program
5 editions published in 1979 in English and held by 62 WorldCat member libraries worldwide
By perturbing a linear program to a quadratic program, it is possible to solve the latter in its dual variable space by iterative techniques such as successive overrelaxation (SOR) methods. This solution provides a solution to the original linear program
Computational optimization : a tribute to Olvi Mangasarian(
Book
)
2 editions published in 1999 in English and held by 40 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 40 WorldCat member libraries worldwide
Error bounds for nondegenerate monotone linear complementarity problems by
Olvi L Mangasarian(
Book
)
7 editions published between 1985 and 1988 in English and held by 10 WorldCat member libraries worldwide
The authors give a bound on the distance between an arbitrary point and the solution set of a monotone linear complementarity problem in terms of a condition constant which depends on the problem data only and a residual function of the violations of the complementarity problem conditions by the point considered. When the point satisfies the linear inequalities of the complementarity problem, the residual consists of the complementarity condition x(Mx + q) plus its square root: (x(Mx + q)) to the 1/2 power. This latter term is essential and without which the error bound cannot hold. It is also shown that another natural residual that has been employed to bound errors for strictly monotone linear complementarity problems, fails to bound errors for the monotone case considered here. Keywords: Mathematical programming; Convex programming. (Author)
7 editions published between 1985 and 1988 in English and held by 10 WorldCat member libraries worldwide
The authors give a bound on the distance between an arbitrary point and the solution set of a monotone linear complementarity problem in terms of a condition constant which depends on the problem data only and a residual function of the violations of the complementarity problem conditions by the point considered. When the point satisfies the linear inequalities of the complementarity problem, the residual consists of the complementarity condition x(Mx + q) plus its square root: (x(Mx + q)) to the 1/2 power. This latter term is essential and without which the error bound cannot hold. It is also shown that another natural residual that has been employed to bound errors for strictly monotone linear complementarity problems, fails to bound errors for the monotone case considered here. Keywords: Mathematical programming; Convex programming. (Author)
Optimal simplex tableau characterization of unique and bounded solutions of linear programs by
Olvi L Mangasarian(
Book
)
5 editions published in 1980 in English and held by 8 WorldCat member libraries worldwide
Uniqueness and boundedness of solutions of linear programs are characterized in terms of an optimal simplex tableau. Let M denote the submatrix in an optimal simplex tableau with columns corresponding to degenerate optimal dual basic variables. A primal optimal solution is unique if and only if there exists a nonvacuous nonnegative linear combination of the rows of M corresponding to degenerate optimal primal basic variables which is positive. The set of primal optimal solutions is bounded if and only if there exists a nonnegative linear combination of the rows of M which is positive. When M is empty the primal optimal solution is unique. (Author)
5 editions published in 1980 in English and held by 8 WorldCat member libraries worldwide
Uniqueness and boundedness of solutions of linear programs are characterized in terms of an optimal simplex tableau. Let M denote the submatrix in an optimal simplex tableau with columns corresponding to degenerate optimal dual basic variables. A primal optimal solution is unique if and only if there exists a nonvacuous nonnegative linear combination of the rows of M corresponding to degenerate optimal primal basic variables which is positive. The set of primal optimal solutions is bounded if and only if there exists a nonnegative linear combination of the rows of M which is positive. When M is empty the primal optimal solution is unique. (Author)
Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems by
Olvi L Mangasarian(
Book
)
6 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide
It is shown that solutions of linear inequalities, linear programs and certain linear complementarity problems (e.g. those with Pmatrices or Zmatrices but not semidefinite matrices) are Lipschitz continuous with respect to changes in the right hand side data of the problem. Solutions of linear programs are not Lipschitz continuous with respect to the coefficients of the objective function. The Lipschitz constant given here is a generalization of the role played by the norm of the inverse of a nonsingular matrix in bounding the perturbation of the solution of a system of equations in terms of a right hand side perturbation. Keywords: Optimization. (Author)
6 editions published in 1985 in English and held by 7 WorldCat member libraries worldwide
It is shown that solutions of linear inequalities, linear programs and certain linear complementarity problems (e.g. those with Pmatrices or Zmatrices but not semidefinite matrices) are Lipschitz continuous with respect to changes in the right hand side data of the problem. Solutions of linear programs are not Lipschitz continuous with respect to the coefficients of the objective function. The Lipschitz constant given here is a generalization of the role played by the norm of the inverse of a nonsingular matrix in bounding the perturbation of the solution of a system of equations in terms of a right hand side perturbation. Keywords: Optimization. (Author)
Dual, feasible direction algorithms by
Olvi L Mangasarian(
Book
)
5 editions published in 1972 in English and Undetermined and held by 7 WorldCat member libraries worldwide
An algorithm for the solution of nonlinearly constrained optimization problems with essentially nonnegativity constraints only. The quadratic subproblems are solved by principal pivoting or other fast quadratic methods. A new method for preventing jamming (or zigzagging) is proposed. Also a general convergence theorem for optimization algorithms is given using the concept of a general necessary optimality function and incorporating the antijamming feature. All algorithms work under a choice of a number of step size selection methods. (Author)
5 editions published in 1972 in English and Undetermined and held by 7 WorldCat member libraries worldwide
An algorithm for the solution of nonlinearly constrained optimization problems with essentially nonnegativity constraints only. The quadratic subproblems are solved by principal pivoting or other fast quadratic methods. A new method for preventing jamming (or zigzagging) is proposed. Also a general convergence theorem for optimization algorithms is given using the concept of a general necessary optimality function and incorporating the antijamming feature. All algorithms work under a choice of a number of step size selection methods. (Author)
Leastnorm linear programming solution as an unconstrained minimization problem by
Olvi L Mangasarian(
Book
)
4 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
It is shown that the dual of the problem of minimizing the 2norm of the primal and dual optimal variables and slacks of a linear program, can be transformed into an unconstrained minimization of a convex, parameterfree, globally differentiable, piecewise quadratic function with a Lipschitz continuous gradient. If the slacks are not included in the norm minimization, one obtains a minimization problem with a convex, parameterfree, quadratic objective function subject to nonnegativity constraints only. (Author)
4 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
It is shown that the dual of the problem of minimizing the 2norm of the primal and dual optimal variables and slacks of a linear program, can be transformed into an unconstrained minimization of a convex, parameterfree, globally differentiable, piecewise quadratic function with a Lipschitz continuous gradient. If the slacks are not included in the norm minimization, one obtains a minimization problem with a convex, parameterfree, quadratic objective function subject to nonnegativity constraints only. (Author)
A stable theorem of the alternative : an extension of the Gordan theorem by
Olvi L Mangasarian(
Book
)
5 editions published in 1981 in English and held by 7 WorldCat member libraries worldwide
A theorem with a number of equivalent alternatives is proposed as an extension of the classical Gordan theorem of the alternative. The theorem can handle nonzero unrestricted variables which cannot be directly treated by ordinary theorems of the alternative. Like the Gordan theorem, the extended theorem has the stability feature that small perturbations in the data will not invalidate an alternative that is in force. The theorem has useful applications in establishing the boundedness and uniqueness of feasible points of polyhedral sets and of solutions to linear programming problems. (Author)
5 editions published in 1981 in English and held by 7 WorldCat member libraries worldwide
A theorem with a number of equivalent alternatives is proposed as an extension of the classical Gordan theorem of the alternative. The theorem can handle nonzero unrestricted variables which cannot be directly treated by ordinary theorems of the alternative. Like the Gordan theorem, the extended theorem has the stability feature that small perturbations in the data will not invalidate an alternative that is in force. The theorem has useful applications in establishing the boundedness and uniqueness of feasible points of polyhedral sets and of solutions to linear programming problems. (Author)
Simple Computable Bounds for Solutions of Linear Complementarity Problems and Linear Programs by
Olvi L Mangasarian(
Book
)
5 editions published in 1983 in English and held by 6 WorldCat member libraries worldwide
Surprisingly simple bounds are given for solutions of fundamental constrained optimization problems such as linear and convex quadratic programs. It is shown that every nonoptimal primaldual feasible point carries within it simple numerical information which bounds some or all components of all solution vectors. The results given permit one to compute bounds without even solving the optimization problems. (Author)
5 editions published in 1983 in English and held by 6 WorldCat member libraries worldwide
Surprisingly simple bounds are given for solutions of fundamental constrained optimization problems such as linear and convex quadratic programs. It is shown that every nonoptimal primaldual feasible point carries within it simple numerical information which bounds some or all components of all solution vectors. The results given permit one to compute bounds without even solving the optimization problems. (Author)
Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs by
Olvi L Mangasarian(
Book
)
6 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide
A parallel successive overrelaxation (SOR) method is proposed for the solution of the fundamental symmetric linear complementarity problem. Convergence is established under a relaxation factor which approaches the classical value of 2 for a loosely coupled problem. The parallel SOR algorithm is then applied to solve the symmetric linear complementarity problem associated with the least norm solution of a linear program
6 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide
A parallel successive overrelaxation (SOR) method is proposed for the solution of the fundamental symmetric linear complementarity problem. Convergence is established under a relaxation factor which approaches the classical value of 2 for a loosely coupled problem. The parallel SOR algorithm is then applied to solve the symmetric linear complementarity problem associated with the least norm solution of a linear program
New error bounds for the linear complementarity problem by
Olvi L Mangasarian(
Book
)
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a 'best' error bound emerges from our comparison as the sum of two natural residuals."
3 editions published in 1993 in English and held by 6 WorldCat member libraries worldwide
Abstract: "New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a 'best' error bound emerges from our comparison as the sum of two natural residuals."
Mathematical programming in neural networks by
Olvi L Mangasarian(
Book
)
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "This paper highlights the role of mathematical programming, particularly linear programming, in training neural networks. A neural network description is given in terms of separating planes in the input space that suggests the use of linear programming for determining these planes. A more standard description in terms of a mean square error in the output space is also given, which leads to the use of unconstrained minimization techniques for training a neural network. The linear programming approach is demonstrated by a brief description of a system for breast cancer diagnosis that has been in use for the last four years at a major medical facility."
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "This paper highlights the role of mathematical programming, particularly linear programming, in training neural networks. A neural network description is given in terms of separating planes in the input space that suggests the use of linear programming for determining these planes. A more standard description in terms of a mean square error in the output space is also given, which leads to the use of unconstrained minimization techniques for training a neural network. The linear programming approach is demonstrated by a brief description of a system for breast cancer diagnosis that has been in use for the last four years at a major medical facility."
Cancer diagnosis via linear programming by
Olvi L Mangasarian(
Book
)
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Abstract: "This report describes informally a diagnostic system that has been in operation at University of Wisconisn [sic] Hospitals for the past 17 months. The system, which has correctly diagnosed 165 out of 166 cases in that period, is based on linear programming and can also be viewed as a neural network."
3 editions published in 1990 in English and held by 5 WorldCat member libraries worldwide
Abstract: "This report describes informally a diagnostic system that has been in operation at University of Wisconisn [sic] Hospitals for the past 17 months. The system, which has correctly diagnosed 165 out of 166 cases in that period, is based on linear programming and can also be viewed as a neural network."
Multicategory discrimination via linear programming by
Kevin P Bennett(
Book
)
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "A single linear program is proposed for discriminating between the elements of k disjoint point sets in the ndimensional real space R[superscript n]. When the conical hulls of the k sets are (k1) point disjoint in R[superscript n+1], a kpiece piecewiselinear surface generated by the linear program completely separates the k sets. This improves on a previous linear programming approach which required that each set be linearly separable from the remaining k1 sets. When the conical hulls of the k sets are not (k1)point disjoint, the proposed linear program generates an errorminimizing piecewiselinear separator for the k sets
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abstract: "A single linear program is proposed for discriminating between the elements of k disjoint point sets in the ndimensional real space R[superscript n]. When the conical hulls of the k sets are (k1) point disjoint in R[superscript n+1], a kpiece piecewiselinear surface generated by the linear program completely separates the k sets. This improves on a previous linear programming approach which required that each set be linearly separable from the remaining k1 sets. When the conical hulls of the k sets are not (k1)point disjoint, the proposed linear program generates an errorminimizing piecewiselinear separator for the k sets
A variable complexity norm maximization problem by
Olvi L Mangasarian(
Book
)
5 editions published between 1984 and 1985 in English and held by 5 WorldCat member libraries worldwide
The solution set to many important constrained optimization problems is a set that is bounded by planes. When such a set is bounded it is useful to find the size of a largest element in that set. In this work we show that this problem may be extremely easy or difficult depending on the measure of size (norm) employed. For one such measure the problem is relatively easy while for all other measures it is intractable. However the problem of merely finding an upper bound for the size of the largest element turns out to be a surprisingly simple problem that can be solved by a single linear program. Keywords include: Optimization, maximum norm, complexity theory, NPcomplete
5 editions published between 1984 and 1985 in English and held by 5 WorldCat member libraries worldwide
The solution set to many important constrained optimization problems is a set that is bounded by planes. When such a set is bounded it is useful to find the size of a largest element in that set. In this work we show that this problem may be extremely easy or difficult depending on the measure of size (norm) employed. For one such measure the problem is relatively easy while for all other measures it is intractable. However the problem of merely finding an upper bound for the size of the largest element turns out to be a surprisingly simple problem that can be solved by a single linear program. Keywords include: Optimization, maximum norm, complexity theory, NPcomplete
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Robinson, Stephen M. Editor
 Meyer, Robert R. Editor
 University of WisconsinMadison Computer Sciences Department Editor
 Association for Computing Machinery Special Interest Group on Mathematical Programming
 Rosen, J. B. (Judah Ben) 1922 Author Editor
 Ritter, K. (Klaus) 1936 Editor
 Ferris, Michael C. Author
 University of WisconsinMadison Mathematics Research Center
 Wright, Stephen J. 1960
 Pang, JongShi
Useful Links
Associated Subjects
Algebras, Linear Algorithms Artificial intelligence CancerDiagnosis Differential equations, Linear Economics Engineering mathematics Errors Expert systems (Computer science) Inequalities (Mathematics) Information theory Iterative methods (Mathematics) Linear complementarity problem Linear programming Linear programmingData processing Mathematical optimization Mathematical optimizationData processing Mathematics MATLAB Neural circuitry Neural networks (Computer science) Nonlinear programming Nonlinear programmingData processing Nonlinear theories Perturbation (Mathematics) Programming (Mathematics) Quadratic programming Relaxation methods (Mathematics) Simplexes (Mathematics)
Alternative Names
Mangasarian, O. L.
Mangasarian, O. L. 1934
Mangasarian, O. L. (Olvi L.), 1934
Mangasarian, Olvi 1934
Mangasarian, Olvi Leon 1934
Olvi Mangasarian American mathematician
Olvi Mangasarian Amerikaans wiskundige
Olvi Mangasarian USamerikanischer Mathematiker und Informatiker
マンガサリアン, O. L
Languages
Covers