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40
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Partitioning mathematical programs for parallel solution
, 1994
"... This paper describes heuristics for partitioning a general M x N matrix into arrowhead form. Such heuristics are useful for decomposing large, constrained, optimization problems into forms that are amenable to parallel processing. The heuristics presented can be easily implemented using publicly ava ..."
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Cited by 28 (0 self)
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This paper describes heuristics for partitioning a general M x N matrix into arrowhead form. Such heuristics are useful for decomposing large, constrained, optimization problems into forms that are amenable to parallel processing. The heuristics presented can be easily implemented using publicly available graph partitioning algorithms. The application of such techniques for solving large linear programs is described. Extensive computational results on the effectiveness of our partitioning procedures and their usefulness for parallel optimization are presented. @ 1998 The
A Pathsearch Damped Newton Method for Computing General Equilibria
 Annals of Operations Research
, 1994
"... Computable general equilibrium models and other types of variational inequalities play a key role in computational economics. This paper describes the design and implementation of a pathsearchdamped Newton method for solving such problems. Our algorithm improves on the typical Newton method (which ..."
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Cited by 22 (11 self)
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Computable general equilibrium models and other types of variational inequalities play a key role in computational economics. This paper describes the design and implementation of a pathsearchdamped Newton method for solving such problems. Our algorithm improves on the typical Newton method (which generates and solves a sequence of LCP's) in both speed and robustness. The underlying complementarity problem is reformulated as a normal map so that standard algorithmic enchancements of Newton's method for solving nonlinear equations can be easily applied. The solver is implemented as a GAMS subsystem, using an interface library developed for this purpose. Computational results obtained from a number of test problems arising in economics are given.
A Computational View of InteriorPoint Methods for Linear Programming
 IN: ADVANCES IN LINEAR AND INTEGER PROGRAMMING
, 1994
"... Many issues that are crucial for an efficient implementation of an interior point algorithm are addressed in this paper. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it so efficient in practice are discussed in detail. Those include: the preprocessing te ..."
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Cited by 17 (10 self)
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Many issues that are crucial for an efficient implementation of an interior point algorithm are addressed in this paper. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it so efficient in practice are discussed in detail. Those include: the preprocessing techniques, the initialization approaches, the methods of computing search directions (and lying behind them linear algebra techniques), centering strategies and methods of stepsize selection. Several reasons for the manifestations of numerical difficulties like e.g.: the primal degeneracy of optimal solutions or the lack of feasible solutions are explained in a comprehensive way. A motivation for obtaining an optimal basis is given and a practicable algorithm to perform this task is presented. Advantages of different methods to perform postoptimal analysis (applicable to interior point optimal solutions) are discussed. Important questions that still remain open in the implementations of i...
A Taxonomy of Advanced Linear Programming Techniques and the Theater Attack Model
 MASTERS THESIS IN OPERATIONS RESEARCH, AIR FORCE INSTITUTE OF TECHNOLOGY
, 1989
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Regularized Decomposition of Stochastic Programs: Algorithmic Techniques and Numerical Results
, 1993
"... A finitely convergent nonsimplex method for large scale structured linear programming problems arising in stochastic programming is presented. The method combines the ideas of the DantzigWolfe decomposition principle and modern nonsmooth optimization methods. Algorithmic techniques taking advantag ..."
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Cited by 8 (1 self)
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A finitely convergent nonsimplex method for large scale structured linear programming problems arising in stochastic programming is presented. The method combines the ideas of the DantzigWolfe decomposition principle and modern nonsmooth optimization methods. Algorithmic techniques taking advantage of properties of stochastic programs are described and numerical results for large real world problems reported.
Dynamic factorization in largescale optimization
 Math. Programming
, 1994
"... Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generatedfrom the remainingexplicit part. Dynamicfactorization admits algebraicelementswhichchangeindimensionduring the courseof solution.A unifyingmathematical framework for dy ..."
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Cited by 8 (1 self)
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Factorization of linear programming (LP) models enables a large portion of the LP tableau to be represented implicitly and generatedfrom the remainingexplicit part. Dynamicfactorization admits algebraicelementswhichchangeindimensionduring the courseof solution.A unifyingmathematical framework for dynamic row factorization is presented with three algorithms which derive from differentLP modelrowstructures:generalizedupperboundrows,purenetworkrows,and generalized networkTOWS. Eachof these structuresis a generalization of its predecessors, andeach corresponding algorithm exhibits just enough additional richness to accommodate the structure at hand within the unifledframework. Implementation andcomputational results arepresentedfor a varietyof realworld models. Theseresultssuggestthateachof thesealgorithmsis superiorto the traditional, nonfactorized approach, with thedegreeof improvement dependingupon thesizeandqualityof the rowfactorization identified.
Solving PiecewiseLinear Programs: Experiments with a Simplex Approach
 ORSA Journal on Computing
, 1992
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GAMS/MINOS: A Solver for Largescale Nonlinear Optimization
 Problemsâ€ť, GAMS Development Corporation
, 2002
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bonsaiG  Algorithms & Design
, 1999
"... This report describes the implementation of bonsaiG, a program for mixedinteger linear programming (MILP). bonsaiG is a research code, designed to explore the utility and power of arc consistency as a general technique for solving MILP problems, and to provide a foundation for exploring other techn ..."
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Cited by 3 (0 self)
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This report describes the implementation of bonsaiG, a program for mixedinteger linear programming (MILP). bonsaiG is a research code, designed to explore the utility and power of arc consistency as a general technique for solving MILP problems, and to provide a foundation for exploring other techniques. It strives to provide maximum flexibility, control, and robustness, while retaining a reasonable level of efificiency. It implements a LPbased branchandbound algorithm and supports binary, general integer, and continuous variables. The underlying LP is an implementation of a dynamic LP algorithm. The tree exploration strategy is depthfirst with bestfirst backtracking. Selection of the next active subproblem is based on a function which can incorporate the objective function and the integer infeasibility of a subproblem. The branching algorithm allows the specification of priorities for selecting branching variables, and the specification of groups of integer variables which are e...