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LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is descr ..."
Abstract

Cited by 74 (11 self)
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An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
The Simplex Algorithm Extended to PiecewiseLinearly Constrained Problems
, 2000
"... We present an extension of the Simplex method for solving problems with piecewiselinear functions of individual variables within the constrains of otherwise linear problems. This work generalizes a previous work of Fourer that accommodate piecewiselinear terms in objective functions. The notio ..."
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Cited by 2 (1 self)
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We present an extension of the Simplex method for solving problems with piecewiselinear functions of individual variables within the constrains of otherwise linear problems. This work generalizes a previous work of Fourer that accommodate piecewiselinear terms in objective functions. The notion of nonbasic variable is extended to a variable fixed at a breakpoint. This new algorithm was implemented through an original extension of the XMP library and successfully applied to solve an industrial problem.
Methods for Convex and General Quadratic Programming ∗
, 2010
"... Computational methods are considered for finding a point that satisfies the secondorder necessary conditions for a general (possibly nonconvex) quadratic program (QP). The first part of the paper defines a framework for the formulation and analysis of feasiblepoint activeset methods for QP. This f ..."
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Computational methods are considered for finding a point that satisfies the secondorder necessary conditions for a general (possibly nonconvex) quadratic program (QP). The first part of the paper defines a framework for the formulation and analysis of feasiblepoint activeset methods for QP. This framework defines a class of methods in which a primaldual search pair is the solution of an equalityconstrained subproblem involving a “working set ” of linearly independent constraints. This framework is discussed in the context of two broad classes of activeset method for quadratic programming: bindingdirection methods and nonbindingdirection methods. We recast a bindingdirection method for general QP first proposed by Fletcher, and subsequently modified by Gould, as a nonbindingdirection method. This reformulation gives the primaldual search pair as the solution of a KKTsystem formed from the QP Hessian and the workingset constraint gradients. It is shown that, under certain circumstances, the solution of this KKTsystem may be updated using a simple recurrence relation, thereby giving a significant reduction in the number of KKT systems that need to be