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21
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
Performance persistence
 Journal of Finance
, 1995
"... Most optimizationbased decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a welldeserved reputation for amplifying small input changes into drastically different solutions. A prev ..."
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Cited by 325 (12 self)
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Most optimizationbased decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a welldeserved reputation for amplifying small input changes into drastically different solutions. A previously optimal solution, or a slight variation of one, may still be nearly optimal in a new scenario and managerially preferable to a dramatically different solution that is mathematically optimal. Mathematical programming models can be stated and solved so that they exhibit varying degrees of persistence with respect to previous values of variables, constraints, or even exogenous considerations. We use case studies to highlight how modeling with persistence has improved managerial acceptance and describe how to incorporate persistence as an intrinsic feature of any optimization model. T^e reasonable man /^ptimizationbased decision support adapts himself to the world; % # V^^'systems, that is, decision support the unreasonable one persists in trvine to adapt i uu J ^U.. iJ. u If systems built around one or more mathethe world to himself; matical programming models, are preTherefore, all progress depends on the unrea j • M I J • n * j i sonable man dominantly employed as follows; A model is used to produce a plan, the plan is pub
A PRACTICAL ANTICYCLING PROCEDURE FOR LINEARLY CONSTRAINED OPTIMIZATION
, 1989
"... A procedure is described for preventing cycling in activeset methods for linearly constrained optimization, including the simplex method. The key ideas are a limited acceptance ofinfeasibilities in all variables, and maintenance of a "working" feasibility tolerance that increases over a l ..."
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Cited by 34 (4 self)
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A procedure is described for preventing cycling in activeset methods for linearly constrained optimization, including the simplex method. The key ideas are a limited acceptance ofinfeasibilities in all variables, and maintenance of a "working" feasibility tolerance that increases over a long sequence of iterations. The additional work per iteration is nominal, and "stalling" cannot occur with exact arithmetic. The method appears to be reliable, based on computational results for the first 53 linear programming problems in the Netlib set.
The gas transmission problem solved by an extension of the simplex algorithm
 Management Science
, 2000
"... The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flowpressure relations, material balances and pressure bounds. The solution method is based on piecewise linear approximations of the nonlinear flowpressure relations. The appro ..."
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Cited by 24 (1 self)
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The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flowpressure relations, material balances and pressure bounds. The solution method is based on piecewise linear approximations of the nonlinear flowpressure relations. The approximated problem is solved by an extension of the Simplex method. The solution method is tested on real world data and compared with alternative solution methods. 1
A DecompositionBased Pricing Procedure for LargeScale Linear Programs: An Application to the Linear Multicommodity Flow Problem
, 2000
"... We propose and test a new pricing procedure for solving largescale structured linear programs. The procedure interactively solves a relaxed subproblem to identify potential entering basic columns. The subproblem is chosen to exploit special structure, rendering it easy to solve. The effect of the p ..."
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Cited by 16 (0 self)
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We propose and test a new pricing procedure for solving largescale structured linear programs. The procedure interactively solves a relaxed subproblem to identify potential entering basic columns. The subproblem is chosen to exploit special structure, rendering it easy to solve. The effect of the procedure is the reduction of the number of pivots needed to solve the problem. Our approach is motivated by the columngeneration approach of DantzigWolfe decomposition. We test our procedure on two sets of multicommodity flow problems. One group of test problems arises in routing telecommunications traffic and the second group is a set of logistics problem which have been widely used to test multicommodity flow algorithms.
Expressing Special Structures in an Algebraic Modeling Language for Mathematical Programming
, 1995
"... A knowledge of the presence of certain special structures can be advantageous in both the formulation and solution of linear programming problems. Thus it is desirable that linear programming software o#er the option of specifying such structures explicitly. As a step in this direction, we describe ..."
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Cited by 14 (4 self)
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A knowledge of the presence of certain special structures can be advantageous in both the formulation and solution of linear programming problems. Thus it is desirable that linear programming software o#er the option of specifying such structures explicitly. As a step in this direction, we describe extensions to an algebraic modeling language that encompass piecewiselinear, network and related structures. Our emphasis is on the modeling considerations that motivate these extensions, and on the design issues that arise in integrating these extensions with the generalpurpose features of the language. We observe that our extensions sometimes make models faster to translate as well as to solve, and that they permit a "columnwise" formulation of the constraints as an alternative to the "rowwise" formulation most often associated with algebraic languages.
DomainIndependent Local Search For Linear Integer Optimization
, 1998
"... Integer and combinatorial optimization problems constitute a major challenge for algorithmics. They arise when a large number of discrete organizational decisions have to be made, subject to constraints and optimization criteria. This thesis ..."
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Cited by 10 (1 self)
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Integer and combinatorial optimization problems constitute a major challenge for algorithmics. They arise when a large number of discrete organizational decisions have to be made, subject to constraints and optimization criteria. This thesis
LP probing for piecewise linear optimization in scheduling
 THIRD INTERNATIONAL WORKSHOP ON INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING FOR COMBINATORIAL OPTIMIZATION PROBLEMS (CPAIOR’01
, 2001
"... A scheduling problem with piecewise linear (PL) optimization extends conventional scheduling by imposing a conjunction of combinatorial PL constraints involving the objective function variables. The problem is decomposed into two constraint subproblems 1) Resource feasibility constraints and 2) Tem ..."
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Cited by 9 (3 self)
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A scheduling problem with piecewise linear (PL) optimization extends conventional scheduling by imposing a conjunction of combinatorial PL constraints involving the objective function variables. The problem is decomposed into two constraint subproblems 1) Resource feasibility constraints and 2) Temporal and PL constraints. This decomposition is fully exploited to apply a probe backtrack algorithm which hybridizes constraint reasoning and Linear Programming (LP) based probing. The paper investigates and compares dierent probing techniques and use the PL constraints can be used to tighten dynamically the subproblem delegated to the prober.
Solving PiecewiseLinear Programs: Experiments with a Simplex Approach
 ORSA Journal on Computing
, 1992
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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 6 (3 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.