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963
Engineering and economic applications of complementarity problems
 SIAM Review
, 1997
"... Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions f ..."
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Cited by 189 (24 self)
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Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions
Finding Facets of General Integer Knapsacks
"... this paper we present several results that suggest that the lifted knapsack cover approach for binary problems can be extended to general integer programs. We introduce the notion of a general integer knapsack cover, and corresponding valid inequalities, demonstrably stronger than those previously k ..."
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known. By an appropriate minimality condition, we show that these inequalities are facet1 defining for the general integer knapsack polytope. We then present another class of inequalities which are facetdefining under less restrictive conditions. We conclude by presenting extended general integer
Generating facets for the independence system polytope
, 2009
"... In this paper, we present procedures to obtain facetdefining inequalities for the independence system polytope. These procedures are defined for inequalities which are not necessarily rank inequalities. We illustrate the use of these procedures by deriving strong valid inequalities for the acyclic ..."
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induced subgraph, triangle free induced subgraph, bipartite induced subgraph, and knapsack polytopes. Finally, we derive a new family of facetdefining inequalities for the independence system polytope by adding a set of edges to antiwebs.
Separation algorithms for 01 knapsack polytopes
, 2008
"... Valid inequalities for 01 knapsack polytopes often prove useful when tackling hard 01 Linear Programming problems. To use such inequalities effectively, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We show that the separation problems for the soca ..."
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Cited by 17 (0 self)
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Valid inequalities for 01 knapsack polytopes often prove useful when tackling hard 01 Linear Programming problems. To use such inequalities effectively, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We show that the separation problems for the so
Lifting Cover Inequalities for the Binary Knapsack Polytope
"... We consider the family of facets of the binary knapsack polytope from minimal covers. We study previous results on sequential lifting in a unifying framework and explore a class of most violated fractional lifted cover inequalities, defined by Balas and Zemel, which are more general than traditional ..."
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We consider the family of facets of the binary knapsack polytope from minimal covers. We study previous results on sequential lifting in a unifying framework and explore a class of most violated fractional lifted cover inequalities, defined by Balas and Zemel, which are more general than
Effective lattice point counting in rational convex polytopes
 JOURNAL OF SYMBOLIC COMPUTATION
, 2003
"... This paper discusses algorithms and software for the enumeration of all lattice points inside a rational convex polytope: we describe LattE, a computer package for lattice point enumeration which contains the first implementation of A. Barvinok's algorithm [8]. We report on computational experi ..."
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Cited by 98 (14 self)
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experiments with multiway contingency tables, knapsack type problems, rational polygons, and flow polytopes. We prove that this kind of symbolicalgebraic ideas surpasses the traditional branchandbound enumeration and in some instances LattE is the only software capable of counting. Using LattE, we have
Combinatorial auctions: A survey
, 2000
"... Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items ..."
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Cited by 212 (1 self)
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Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles
A Polyhedral Study of the Cardinality Constrained Knapsack Problem
, 2001
"... A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas as finance, location, and scheduling. Traditionally, cardinality constraints are mode ..."
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Cited by 11 (1 self)
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A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas as finance, location, and scheduling. Traditionally, cardinality constraints
Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
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Cited by 221 (14 self)
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One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, machine learning, control theory, and numerous other areas. The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in symbolic algebra and numerical software for geometric calculations have revolutionized the field, making formerly inaccessible problems tractable, and providing fertile ground for experimentation and conjecture. The first half of this book furnishes an introduction and represents a snapshot of the state of the art regarding systems of polynomial equations. Afficionados of the wellknown text books by Cox, Little, and O’Shea will find familiar themes in the first five chapters: polynomials in one variable, Gröbner
Results 11  20
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963