Mangasarian, Olvi L. 1934Overview
Publication Timeline
Most widely held works by
Olvi L Mangasarian
Nonlinear programming
by Olvi L Mangasarian
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Book
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38 editions published between 1969 and 1994 in English and Undetermined and held by 776 WorldCat member libraries worldwide This reprint of the 1969 book of the same name 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. Properties of differentiable convex functions are derived and then used in two key chapters of the book, one on optimality conditions for differentiable nonlinear programs and one on duality in nonlinear programming. Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints. The book has four useful selfcontained appendices on vectors and matrices, topological properties of ndimensional real space, continuity and minimization, and differentiable functions
Nonlinear programming; proceedings
by Wis.) Symposium on Nonlinear Programming$(1970 : Madison
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Book
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17 editions published between 1970 and 1975 in English and Undetermined and held by 370 WorldCat member libraries worldwide
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
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Book
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5 editions published in 1975 in English and held by 258 WorldCat member libraries worldwide
Linear programming with MATLAB
by Michael C Ferris
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Book
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12 editions published in 2007 in English and held by 254 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
Nonlinear programming 3 : proceedings of the Special Interest Group on Mathematical Programming symposium
by Olvi L Mangasarian
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Book
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7 editions published in 1978 in English and Undetermined and held by 177 WorldCat member libraries worldwide
Nonlinear programming 4 : proceedings of the Nonlinear Programming Symposium 4
by Nonlinear Programming Symposium
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Book
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6 editions published in 1981 in English and held by 167 WorldCat member libraries worldwide An upper triangular matrix method for quadratic programming; Solving quadratic programs by an exact penalty function; QPBased methods for largescale nonlinearly constrained optimization; Numerical experiments with an exact L1, penalty function method; An iterative linear programming algorithm based on an augmented lagrangian; Iterative algorithms for singular minimization problems; A new derivation of symmetric positive definite secant updates; On preconditioned conjugate gradient method; Finding the global minimum of a function of one variable using the methods of constant signed higher order derivatives; On a bundle algorithms for nonsmooth optimization; Convergence results in a class of variable metric subgradient methods; Monotropic programming: descent algorithms and duality
Complementarity : applications, algorithms, and extensions
by Michael C Ferris
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Book
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4 editions published between 2001 and 2011 in English and held by 70 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."BOOK JACKET
Iterative solution of linear programs
by Olvi L Mangasarian
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Book
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3 editions published in 1979 in English and held by 53 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
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Book
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1 edition published in 1999 in English and held by 38 WorldCat member libraries worldwide
Error bounds for nondegenerate monotone linear complementarity problems
by Olvi L Mangasarian
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Book
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6 editions published between 1985 and 1988 in English and held by 9 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)
Nonlinear programming : proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin, Madison May 4  6, 1970
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Book
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1 edition published in 1970 in English and held by 8 WorldCat member libraries worldwide
Nonlinear programming, 3 / proceedings of the Special Interest Group on Mathematical Programming symposium, conducted by the Computer Sciences Department at the University of WisconsinMadison, July 1113, 1977
by Symposium on Nonlinear Programming
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Book
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3 editions published in 1978 in English and Undetermined and held by 7 WorldCat member libraries worldwide
Optimal simplex tableau characterization of unique and bounded solutions of linear programs
by Olvi L Mangasarian
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Book
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3 editions published in 1980 in English and held by 6 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)
Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem
by R De Leone
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Book
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3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
A Condition Number for Linear Inequalities and Linear Programs
by Olvi L Mangasarian
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Book
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5 editions published in 1981 in English and Undetermined and held by 5 WorldCat member libraries worldwide A new explicit bound is given for the ratio of the absolute error in an approximate solution of a system of linear inequalities and equalities to the absolute residual. This bound generalizes the concept of a norm of the inverse of a nonsingular matrix. With this bound a condition number is defined for a system of linear inequalities and equalities and for linear programs. The condition number gives a bound on the ratio of the relative error of an approximate solution to the relative residual. In the case of a strongly stable system of linear inequalities and equalities the condition number can be computed by means of a single linear program. (Author)
Dual, feasible direction algorithms
by Olvi L Mangasarian
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Book
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3 editions published in 1972 in English and Undetermined and held by 5 WorldCat member libraries worldwide
New error bounds for the linear complementarity problem
by Olvi L Mangasarian
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Book
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2 editions published in 1993 in English and held by 5 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."
A stable theorem of the alternative : an extension of the Gordan theorem
by Olvi L Mangasarian
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Book
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4 editions published in 1981 in English and held by 5 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)
Leastnorm linear programming solution as an unconstrained minimization problem
by Olvi L Mangasarian
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Book
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3 editions published in 1980 in English and held by 5 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)
Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems
by Olvi L Mangasarian
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Book
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4 editions published in 1985 in English and held by 5 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) more
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Algebras, Linear Algorithms Artificial intelligence Convergence Differential equations, Linear Economics Engineering mathematics Errors Inequalities (Mathematics) Information theory Iterative methods (Mathematics) Linear complementarity problem Linear programming Linear programmingData processing Mathematical optimization Mathematical optimizationData processing Mathematics MATLAB 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 Leon 1934
マンガサリアン, O. L
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