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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
Fast Heuristics for the Maximum Feasible Subsystem Problem
 INFORMS Journal on Computing
, 2001
"... Given an infeasible set of linear constraints, finding the maximum cardinality feasible subsystem is known as the maximum feasible subsystem problem. This problem is known to be NPhard, but has many practical applications. This paper presents improved heuristics for solving the maximum feasible sub ..."
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Cited by 24 (0 self)
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Given an infeasible set of linear constraints, finding the maximum cardinality feasible subsystem is known as the maximum feasible subsystem problem. This problem is known to be NPhard, but has many practical applications. This paper presents improved heuristics for solving the maximum feasible subsystem problem that are significantly faster than the original, but still highly accurate.
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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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.
A Branch and Cut Algorithm for the Halfspace Depth Problem∗
"... The concept of data depth in nonparametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the halfspace depth (or rank) of p is defined as the minimum n ..."
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The concept of data depth in nonparametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the halfspace depth (or rank) of p is defined as the minimum number of points of S contained in any closed halfspace with p on its boundary. Computing halfspace depth is NPhard, and it is equivalent to the Maximum Feasible Subsystem problem. In this paper a mixed integer program is formulated with the bigM method for the halfspace depth problem. We suggest a branch and cut algorithm for these integer programs. In this algorithm, Chinneck’s heuristic algorithm is used to find an upper bound and a related technique based on sensitivity analysis is used for branching. Irreducible Infeasible Subsystem (IIS) hitting set cuts are applied. We also suggest a binary search algorithm which may be more numerically stable. The algorithms are implemented with the BCP framework from the COINOR project. 1
Annual Scheduling of Atlantic Fleet Naval Combatants
, 1985
"... Approved for public release; distribution is unlimited. 17. DISTRIBUTION STATEMENT (ol the abetract entered In Block 30. II different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse aide If neceaaary and Identify by block number) employment scheduling, integer programming, se ..."
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Approved for public release; distribution is unlimited. 17. DISTRIBUTION STATEMENT (ol the abetract entered In Block 30. II different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse aide If neceaaary and Identify by block number) employment scheduling, integer programming, set covering, math programming, column generation 20. ABSTRACT (Continue on reveree aide It neceaaary and Identity by block number) Employment Scheduling is the task of assigning ships to fullfil 0. S. Navy commitments at home and abroad. Commitments are events, with fixed start and completion dates, that require specified ship resources. The objective of the employment schedule is to satisfy all event requirements while providing an equitable rotation of ships and an even distribution of workload. This study provides a mathematical programming model to assist employDD
Integrated Classifier Hyperplane Placement and Feature Selection
, 2011
"... Errata are shown in red. The process of placing a separating hyperplane for data classification is normally disconnected from the process of selecting the features to use. An approach for feature selection that is conceptually simple but computationally explosive is to simply apply the hyperplane pl ..."
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Errata are shown in red. The process of placing a separating hyperplane for data classification is normally disconnected from the process of selecting the features to use. An approach for feature selection that is conceptually simple but computationally explosive is to simply apply the hyperplane placement process to all possible subsets of features, selecting the smallest set of features that provides reasonable classification accuracy. Two ways to speed this process are (i) use a faster filtering criterion instead of a complete hyperplane placement, and (ii) use a greedy forward or backwards sequential selection method. This paper introduces a new filtering criterion that is very fast: maximizing the drop in the sum of infeasibilities in a linearprogramming transformation of the problem. It also shows how the linear programming transformation can be applied to reduce the number of features after a separating hyperplane has already been placed while maintaining the separation that was originally induced by the hyperplane. Finally, a new and highly effective integrated method that simultaneously selects features while placing the separating hyperplane is introduced. 1.
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