Results 1 
5 of
5
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 ..."
Abstract

Cited by 93 (15 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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 ..."
Abstract
 Add to MetaCart
(Show Context)
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
Optimal Decisions from Probabilistic Models: the IntersectionoverUnion Case
"... A probabilistic model allows us to reason about the world and make statistically optimal decisions using Bayesian decision theory. However, in practice the intractability of the decision problem forces us to adopt simplistic loss functions such as the 0/1 loss or Hamming loss and as result we make ..."
Abstract
 Add to MetaCart
(Show Context)
A probabilistic model allows us to reason about the world and make statistically optimal decisions using Bayesian decision theory. However, in practice the intractability of the decision problem forces us to adopt simplistic loss functions such as the 0/1 loss or Hamming loss and as result we make poor decisions through MAP estimates or through loworder marginal statistics. In this work we investigate optimal decision making for more realistic loss functions. Specifically we consider the popular intersectionoverunion (IoU) score used in image segmentation benchmarks and show that it results in a hard combinatorial decision problem. To make this problem tractable we propose a statistical approximation to the objective function, as well as an approximate algorithm based on parametric linear programming. We apply the algorithm on three benchmark datasets and obtain improved intersectionoverunion scores compared to maximumposteriormarginal decisions. Our work points out the difficulties of using realistic loss functions with probabilistic computer vision models. 1.
Methods for Convex and General Quadratic Programming∗
, 2014
"... 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 considers the formulation and analysis of an activeset method for a generic QP with both equality and ..."
Abstract
 Add to MetaCart
(Show Context)
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 considers the formulation and analysis of an activeset method for a generic QP with both equality and inequality constraints. The method uses a search direction that is the solution of an equalityconstrained subproblem involving a “working set ” of linearly independent constraints. The method is a reformulation of a method for general QP first proposed by Fletcher, and modified subsequently by Gould. The reformulation facilitates a simpler analysis and has the benefit that the algorithm reduces to a variant of the simplex method when the QP is a linear program. The search direction is computed from a KKT system formed from the QP Hessian and the gradients of the workingset constraints. It is shown that, under certain circumstances, the solution of this KKT system may be updated using a simple recurrence relation, thereby giving a significant reduction in the number of KKT systems that need to be solved. The second part of the paper focuses on the solution of QP problems with constraints in socalled standard form. We describe how the constituent KKT systems are solved, and discuss how an initial basis is defined. Numerical results are presented for all QPs in the CUTEst test collection. Key words. Largescale quadratic programming, activeset methods, convex and nonconvex quadratic programming, KKT systems, Schurcomplement method, variablereduction method.