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Book ChapterDOI

Pathways to the optimal set in linear programming

Nimrod Megiddo
- pp 131-158
TLDR
In this article, the authors present continuous paths leading to the set of optimal solutions of a linear programming problem, which are derived from the weighted logarithmic barrier function and have nice primal-dual symmetry properties.
Abstract: 
This chapter presents continuous paths leading to the set of optimal solutions of a linear programming problem These paths are derived from the weighted logarithmic barrier function The defining equations are bilinear and have some nice primal-dual symmetry properties Extensions to the general linear complementarity problem are indicated

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Citations
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Book

Numerical Optimization

Jorge Nocedal, +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Journal ArticleDOI

A tutorial on support vector regression

Alexander J. Smola, +1 more
- 01 Aug 2004 - 
TL;DR: This tutorial gives an overview of the basic ideas underlying Support Vector (SV) machines for function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.
Book

Linear Programming: Foundations and Extensions

Robert J. Vanderbei
TL;DR: The Simplex Method in Matrix Notation and Duality Theory, and Applications: Foundations of Convex Programming.
BookDOI

Numerical Continuation Methods

Eugene L. Allgower, +1 more
Book ChapterDOI

Knitro: An Integrated Package for Nonlinear Optimization

Richard H. Byrd, +2 more
TL;DR: The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings, and it is effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming.
References
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Book

Linear Programming and Extensions

George B. Dantzig
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Journal ArticleDOI

A new polynomial-time algorithm for linear programming

Narendra Karmarkar
- 01 Dec 1984 - 
TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).
Book

Nonlinear Programming: Sequential Unconstrained Minimization Techniques

Anthony V. Fiacco, +1 more
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.
Journal ArticleDOI

Linear Programming and Extensions. George B. Dantzig. Pp. xvi, 623. 92/- (Princeton Univ. Press). 1963

S. Vajda
- 01 Oct 1965 - 
Journal ArticleDOI

Bimatrix Equilibrium Points and Mathematical Programming

C. E. Lemke
- 01 May 1965 - 
TL;DR: In this paper, simple constructive proofs are given of solutions to the matric matric system Mz − ω = q; z ≧ 0; ω ≧ 1; zT = 0, for various kinds of data M, q, which embrace quadratic programming and the problem of finding equilibrium points of bimatrix games.