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Complementarity and Nondegeneracy in Semidefinite Programming
, 1995
"... Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict complem ..."
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Cited by 111 (9 self)
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Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict
Nondegeneracy of Polyhedra and Linear Programs
, 1995
"... This paper deals with nondegeneracy of polyhedra and linear programming (LP) problems. We allow for the possibility that the polyhedra and the feasible polyhedra of the LP problems under consideration be nonpointed. (A polyhedron is pointed if it has a vertex.) With respect to a given polyhedron, w ..."
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Cited by 1 (1 self)
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, we consider two notions of nondegeneracy and then provide several equivalent characterizations for each of them. With respect to LP problems, we study the notion of constant cost nondegeneracy first introduced by Tsuchiya [25] under a different name, namely dual nondegeneracy. (We do not follow
Remarks On Nondegeneracy In Mixed SemidefiniteQuadratic Programming
, 1998
"... We consider the definitions of nondegeneracy and strict complementarity given in [5] for semidefinite programming (SDP) and their obvious extensions to mixed semidefinitequadratic programming (SDQP). We show that a solution to SDQP satisfies strict complementarity and primal and dual nondegeneracy ..."
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Cited by 2 (0 self)
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We consider the definitions of nondegeneracy and strict complementarity given in [5] for semidefinite programming (SDP) and their obvious extensions to mixed semidefinitequadratic programming (SDQP). We show that a solution to SDQP satisfies strict complementarity and primal and dual
SecondOrder Cone Programming
 MATHEMATICAL PROGRAMMING
, 2001
"... In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic struc ..."
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Cited by 247 (11 self)
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structure that is connected to SOCP. This algebra is a special case of a Euclidean Jordan algebra. After presenting duality theory, complementary slackness conditions, and definitions and algebraic characterizations of primal and dual nondegeneracy and strict complementarity we review the logarithmic
Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming
 SIAM Journal on optimization
, 2009
"... Abstract It is known that the KarushKuhnTucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies, ..."
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Cited by 18 (6 self)
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Abstract It is known that the KarushKuhnTucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies
NONDEGENERACY, FROM THE PROSPECT OF WAVEWAVE REGULAR INTERACTIONS OF A GASDYNAMIC TYPE: SOME REMARKS
"... An analogue of the genuinely nonlinear character of an onedimensional simple waves solution is identified and essentially used in the construction of some multidimensional extensions (simple waves solutions, regular interactions of simple waves solutions). A class of exact multidimensional gasdynam ..."
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Cited by 3 (2 self)
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gasdynamic solutions is constructed whose interactive elements are regular. Some specific aspects of Burnat’s multidimensional “algebraic ” description [which uses a dual connection between the hodograph and physical characteristic details] are identified and classified with an admissibility criterion
An Implementation Of The Dual Affine Scaling Algorithm For Minimum Cost Flow On Bipartite Uncapacitated Networks
 SIAM Journal on Optimization
, 1993
"... . We describe an implementation of the dual affine scaling algorithm for linear programming specialized to solve minimum cost flow problems on bipartite uncapacitated networks. This implementation uses a preconditioned conjugate gradient algorithm to solve the system of linear equations that determi ..."
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Cited by 36 (4 self)
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that determines the search direction at each iteration of the interior point algorithm. Two preconditioners are considered: a diagonal preconditioner and a preconditioner based on the incidence matrix of an approximate maximum weighted spanning tree of the network. Under dual nondegeneracy, this spanning tree
Local Convergence of PredictorCorrector InfeasibleInteriorPoint Algorithms for SDPs and SDLCPs
 Mathematical Programming
, 1997
"... . An example of SDPs (semidefinite programs) exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the MizunoToddYe type predictorcorrector primaldual interiorpoint method for LPs (linear programs) to SDPs, and suggests that we need to force the genera ..."
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Cited by 58 (4 self)
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convergence under strict complementarity and nondegeneracy conditions. Key words. Semidefinite Programming, InfeasibleInteriorPoint Method, PredictorCorrectorMethod, Superlinear Convergence, PrimalDual Nondegeneracy Abbreviated Title. InteriorPoint Algorithms for SDPs y Department of Mathematical
Optimization with Semidefinite, Quadratic and Linear Constraints
 RUTCOR, RUTGERS UNIVERSITY
, 1997
"... We consider optimization problems where variables have either linear, or convex quadratic or semidefinite constraints. First, we define and characterize primal and dual nondegeneracy and strict complementarity conditions. Next, we develop primaldual interior point methods for such problems and show ..."
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Cited by 19 (3 self)
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We consider optimization problems where variables have either linear, or convex quadratic or semidefinite constraints. First, we define and characterize primal and dual nondegeneracy and strict complementarity conditions. Next, we develop primaldual interior point methods for such problems
GLOBAL CONVERGENCE PROPERTY OF THE AFFINE SCALING METHODS FOR PRIMAL DEGENERATE LINEAR PROGRAMMING PROBLEMS
, 1992
"... In this paper we investigate the global convergence property of the affine scaling method under the assumption of dual nondegeneracy. The behavior of the method near degenerate vertices is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous LP proble ..."
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Cited by 13 (6 self)
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In this paper we investigate the global convergence property of the affine scaling method under the assumption of dual nondegeneracy. The behavior of the method near degenerate vertices is analyzed in detail on the basis of the equivalence between the affine scaling methods for homogeneous LP
Results 1  10
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