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590
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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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
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
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
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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's global convergence result on the affine scaling method assuming primal nondegeneracy.
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
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 237 (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
1Nondegeneracy and Inexactness of Semidefinite Relaxations of Optimal Power Flow
"... Abstractâ€”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
Positive semidefinite matrix completions on chordal graphs and the constraint nondegeneracy in semidefinite programming
, 2008
"... LetG = (V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every Gpartial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint n ..."
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Cited by 4 (0 self)
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nondegeneracy condition in semidefinite programming and prove that they are each equivalent to (iii) For any Gpartial positive definite matrix that has a positive semidefinite completion, constraint nondegeneracy is satisfied at each of its positive semidefinite matrix completions.
The primal power affine scaling method
"... In this paper, we present a variant of the primal affine scaling method, which we call the primal power affine scaling method. This method is defined by choosing a real r> 0.5, and is similar to the power barrier variant of the primaldual homotopy methods considered by den Hertog, Roos and Terla ..."
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Cited by 3 (0 self)
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In this paper, we present a variant of the primal affine scaling method, which we call the primal power affine scaling method. This method is defined by choosing a real r> 0.5, and is similar to the power barrier variant of the primaldual homotopy methods considered by den Hertog, Roos
Results 1  10
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590