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5,319
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 110 (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
ADDENDA AND ERRATA FOR ON NONDEGENERACY OF CURVES
"... This note gives some addenda and errata for the article On nondegeneracy of curves [3]. ..."
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This note gives some addenda and errata for the article On nondegeneracy of curves [3].
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 233 (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
Nondegeneracy of the Lie algebra aff(n)
, 2002
"... We show that aff(n), the Lie algebra of affine transformations of R n, is analytically nondegenerate in the sense of A. Weinstein; this means that every analytic Poisson structure vanishing at a point with a linear part corresponding to aff(n) is locally analytically linearizable. ..."
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We show that aff(n), the Lie algebra of affine transformations of R n, is analytically nondegenerate in the sense of A. Weinstein; this means that every analytic Poisson structure vanishing at a point with a linear part corresponding to aff(n) is locally analytically linearizable.
CONSTRAINT NONDEGENERACY, STRONG REGULARITY AND NONSINGULARITY IN SEMIDEFINITE PROGRAMMING
"... 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, the stro ..."
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Cited by 18 (6 self)
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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 Concepts for Zeros of Piecewise Smooth Functions
, 1996
"... A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fr'echet differentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational i ..."
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Cited by 1 (0 self)
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A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fr'echet differentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational
1Nondegeneracy and Inexactness of Semidefinite Relaxations of Optimal Power Flow
"... Abstract—The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex Quadratically Constrained Quadratic Program (QCQP). There is a growing body of work on the use of semidefinite programming relaxations to solve OPF. The relaxation is exact if and only if the corresponding optimal solu ..."
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solution set contains a rankone matrix. In this paper, we establish sufficient conditions guaranteeing the nonexistence of a rankone matrix in said optimal solution set. In particular, we show that under mild assumptions on problem nondegeneracy, any optimal solution to the semidefinite relaxation
On Removing Nondegeneracy Assumptions in Computational Geometry (Extended Abstract)
, 1997
"... ) Francisco G'omez 1 , Suneeta Ramaswami 2 and Godfried Toussaint 2 1 Dept. of Applied Mathematics, Universidad Politecnica de Madrid, Madrid, Spain 2 School of Computer Science, McGill University, Montr'eal, Qu'ebec, Canada Abstract Existing methods for removing degeneracies ..."
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Cited by 9 (7 self)
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address an alternative approach that has received little attention in the computational geometry literature. Often a typical computational geometry paper will make a nondegeneracy assumption that can in fact be removed (without perturbing the input) by a global rigid transformation of the input
Results 1  10
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5,319