WorldCat Identities

Mangasarian, Olvi L. 1934-

Overview
Works: 166 works in 238 publications in 4 languages and 2,342 library holdings
Roles: Editor
Classifications: t57.8, 519.76
Publication Timeline
Key
Publications about Olvi L Mangasarian Publications about Olvi L Mangasarian
Publications by Olvi L Mangasarian Publications by Olvi L Mangasarian
Most widely held works by Olvi L Mangasarian
by ( Book )
21 editions published between and 1994 in English and Undetermined and held by 658 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 self-contained appendices on vectors and matrices, topological properties of n-dimensional real space, continuity and minimization, and differentiable functions.
by ( Book )
3 editions published in in English and held by 313 libraries worldwide
by ( Book )
3 editions published in in English and held by 263 libraries worldwide
by ( Book )
6 editions published in in English and held by 203 libraries worldwide
This textbook provides a self-contained 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, interior-point 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 senior-level undergraduate students, first-year graduate students, and researchers unfamiliar with linear programming.
by ( Book )
3 editions published in in English and held by 172 libraries worldwide
by ( Book )
3 editions published in in English and held by 165 libraries worldwide
by ( Book )
2 editions published in in English and held by 50 libraries worldwide
by ( Book )
3 editions published in in English and Undetermined and held by 5 libraries worldwide
by ( Book )
2 editions published in in English and held by 4 libraries worldwide
by ( Book )
2 editions published in in English and held by 4 libraries worldwide
by ( Book )
1 edition published in in English and held by 4 libraries worldwide
Abstract: "A single linear program is proposed for discriminating between the elements of k disjoint point sets in the n-dimensional real space R[superscript n]. When the conical hulls of the k sets are (k-1)- point disjoint in R[superscript n+1], a k-piece piecewise-linear 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 k-1 sets. When the conical hulls of the k sets are not (k-1)-point disjoint, the proposed linear program generates an error-minimizing piecewise-linear separator for the k sets.
by ( Book )
1 edition published in in English and held by 4 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."
by ( Book )
1 edition published in in English and held by 3 libraries worldwide
 
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Audience Level
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  Kids General Special  
Audience level: 0.78 (from 0.67 for Nonlinear ... to 1.00 for Dual, feas ...)
Complementarity : applications, algorithms, and extensions
Alternative Names
Mangasarian, O. L.
Mangasarian, O. L. 1934-
Mangasarian, O. L. (Olvi L.), 1934-
Mangasarian, Olvi Leon 1934-
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