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Infeasibility certificates for linear matrix inequalities
"... Abstract. Farkas ’ lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebr ..."
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Cited by 3 (1 self)
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Abstract. Farkas ’ lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear
Infeasibility Certificates and the Complexity of the Core in Coalitional Games
"... This paper characterizes the complexity of the core in coalitional games. There are different proposals for representing coalitional games in a compact way, where the worths of coalitions may be computed in polynomial time. In all those frameworks, it was shown that core nonemptiness is a coNPhard ..."
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Cited by 10 (2 self)
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representation of the game where the worths of coalitions may be computed in polynomial time (also, nondeterministic polynomial time), encompassing all previous proposals of this kind. This is proved by showing that games with empty cores have small infeasibility certificates. The picture is completed
Condition and Complexity Measures for Infeasibility Certificates of Systems of Linear Inequalities and Their Sensitivity Analysis
, 2002
"... We begin with a study of the infeasibility measures for linear programming problems. For this purpose, we consider feasibility problems in Karmarkar's standard form. Our main focus is on the complexity measures which can be used to bound the amount of computational effort required to solve syst ..."
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Cited by 1 (1 self)
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We begin with a study of the infeasibility measures for linear programming problems. For this purpose, we consider feasibility problems in Karmarkar's standard form. Our main focus is on the complexity measures which can be used to bound the amount of computational effort required to solve
Computing Infeasibility Certificates for Combinatorial Problems through Hilbert’s Nullstellensatz
, 2009
"... Systems of polynomial equations with coefficients over a field K can be used to concisely model combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3colorable, hamiltonian, etc.) if and only if a related system of polynomial equations has a solution over the a ..."
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Cited by 3 (3 self)
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the algebraic closure of the field K. In this paper, we investigate an algorithm aimed at proving combinatorial infeasibility based on the observed low degree of Hilbert’s Nullstellensatz certificates for polynomial systems arising in combinatorics, and based on fast largescale linearalgebra computations over
Guaranteed Steady State Bounds for Uncertain (Bio)Chemical Processes using Infeasibility Certificates
, 2010
"... Both authors contributed equally. Abstract Analysis and safety considerations of chemical and biological processes require complete knowledge of the set of all feasible steady states. Nonlinearities, uncertain parameters, and discrete variables complicate the task of obtaining this set. In this pape ..."
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version of the corresponding feasibility problem. It uses the Lagrange dual problem to obtain certificates for regions in state space not containing steady states. These infeasibility certificates can be computed efficiently by solving a semidefinite program, rendering the calculation of an outer bounding
Certificates of linear mixed integer infeasibility
, 2008
"... A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, y T A integral such that y T b is fractional. We extend this result to systems that both have equation ..."
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Cited by 3 (3 self)
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equations and inequalities {Ax = b, Cx ≤ d}. We show that a certificate of integral infeasibility is a linear system with rank(C) variables containing no integral point. The result also extends to the mixed integer setting.
Detecting Infeasibility in InfeasibleInteriorPoint Methods for Optimization
 Foundations of Computational Mathematics, Minneapolis 2002, London Mathematical Society Lecture Note Series 312
, 2003
"... We study interiorpoint methods for optimization problems in the case of infeasibility or unboundedness. While many such methods are designed to search for optimal solutions even when they do not exist, we show that they can be viewed as implicitly searching for welldefined optimal solutions to rel ..."
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Cited by 9 (1 self)
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to related problems whose optimal solutions give certificates of infeasibility for the original problem or its dual. Our main development is in the context of linear programming, but we also discuss extensions to more general convex programming problems.
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"... and except as licensed below, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording, or otherwise), without prior written permission of mySecureSign, Inc. Notwithsta ..."
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. Notwithstanding the above, permission is granted to reproduce and distribute this mySecureSign, Inc. Certification Practice Statement on a nonexclusive, royaltyfree basis, provided that (i) the foregoing copyright notice and the beginning paragraphs are prominently displayed at the beginning of each copy
Certificate
, 2010
"... This is to certify that the work in the thesis entitled On Protocols for Information Security Services by Debasish Jena is a record of an original research work carried out by him under my supervision and guidance in partial ..."
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This is to certify that the work in the thesis entitled On Protocols for Information Security Services by Debasish Jena is a record of an original research work carried out by him under my supervision and guidance in partial
Results 1  10
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