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A MIXEDINTEGER LINEAR PROGRAMMING PROBLEM WHICH IS EFFICIENTLY SOLVABLE
, 1987
"... FIELD GROUP SUBGROUP Algorithms, linear programming, mathematical programming, graph theory, shortest paths, combinatorial optimization 19 ABSTRACT (Continue on reverse if necessary and identify by block number) Efficient algorithms are known for the simple linear programming problem where each in ..."
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equality is in the form xjxi. a. Furthermore, these techniques extend to the integer linear programming variant of theiroblem. This paper gives an efficient solution to the mixedinteger linear programming variant where some, but not necessarily all, of the unknoi.ls ire requiired to be integers. The algorithm we
Duality for mixedinteger linear programs
 The International Journal of Operations Research
, 2007
"... AbstractThe theory of duality for linear programs is welldeveloped and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixedinteger linear programs, but this has proven difficult, in part because dua ..."
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Cited by 3 (1 self)
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duality theory does not integrate well with current computational practice. This paper surveys what is known about duality for integer programs and offers some minor extensions, with an eye towards developing a more practical framework. KeywordsDuality, Mixedinteger linear programming, Value function
Minimax Programs
 University of California Press
, 1997
"... We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting spec ..."
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Cited by 475 (5 self)
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special case and present an efficient algorithm for its solution. 1 Introduction Over the last fifty years, thousands of problems of practical interest have been formulated as a linear program. Not only has the linear programming model proven to be widely applicable, but ongoing research has discovered
Automatic Discovery of Linear Restraints Among Variables of a Program
, 1978
"... The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs. ..."
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Cited by 733 (47 self)
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The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs.
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Genetic Programming
, 1997
"... Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring ..."
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Cited by 1051 (12 self)
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Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring
Network formulations of mixedinteger programs
 In preparation
, 2006
"... We consider mixedinteger sets of the type MIX TU = {x: Ax ≥ b; xi integer, i ∈ I}, where A is a totally unimodular matrix, b is an arbitrary vector and I is a nonempty subset of the column indices of A. We show that the problem of checking nonemptiness of a set MIX TU is NPcomplete even in the cas ..."
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Cited by 11 (6 self)
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We consider mixedinteger sets of the type MIX TU = {x: Ax ≥ b; xi integer, i ∈ I}, where A is a totally unimodular matrix, b is an arbitrary vector and I is a nonempty subset of the column indices of A. We show that the problem of checking nonemptiness of a set MIX TU is NPcomplete even
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
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Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
Results 1  10
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710,148