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228
On the Convergence Rate of Newton InteriorPoint Methods in the Absence of Strict Complementarity
 Computational Optimization and Applications
, 1996
"... In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interiorpoint methods for linear complementarity problems is at best linear. They also established an upper bound of 1=4 for the Q 1 factor of the duality gap sequence when the ..."
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Cited by 10 (0 self)
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In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interiorpoint methods for linear complementarity problems is at best linear. They also established an upper bound of 1=4 for the Q 1 factor of the duality gap sequence when
On the Convergence Rate of Newton InteriorPoint Methods in the Absence of Strict Complementarity
 Computational Optimization and Applications
, 1996
"... In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interiorpoint methods for linear complementarity problems is at best linear. They also established an upper bound of 1=4 for the Q 1 factor of the duality gap sequence when the ..."
Abstract
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In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interiorpoint methods for linear complementarity problems is at best linear. They also established an upper bound of 1=4 for the Q 1 factor of the duality gap sequence when
On the local convergence of semismooth Newton methods for linear and nonlinear secondorder cone programs without strict complementarity,
 SIAM Journal on Optimization
, 2009
"... Abstract The optimality conditions of a nonlinear secondorder cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear secondorder cone program. Conditions for the loca ..."
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Cited by 15 (2 self)
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for the local quadratic convergence of these nonsmooth Newton methods are investigated. Related conditions are also given for the special case of a linear secondorder cone program. An interesting and important feature of these conditions is that they do not require strict complementarity of the solution. Some
Superlinear and quadratic convergence of affinescaling interiorpoint Newton methods for problems with simple bounds without strict complementarity assumption
 Math. Programming
, 1999
"... A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong second order sufficient optimality conditions at the solution are satisfied, but strict complementarit ..."
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A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong second order sufficient optimality conditions at the solution are satisfied, but strict
Superlinear and Quadratic Convergence of AffineScaling InteriorPoint Newton Methods for Problems with Simple Bounds without Strict Complementarity Assumption
, 1998
"... A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong... ..."
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Cited by 22 (3 self)
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A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong...
An SQP Feasible Descent Algorithm for Nonlinear Inequality Constrained Optimization Without Strict Complementarity
, 2005
"... ..."
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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complementarity is assumed. Primal and dual nondegeneracy assumptions do not imply strict complementarity, as they do in LP. The primal and dual nondegeneracy assumptions imply a range of possible ranks for primal and dual solutions X and Z. This is in contrast with LP where nondegeneracy assumptions exactly
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
Strict Feasibility Conditions in Nonlinear Complementarity Problems
, 2000
"... The strict feasibility plays an important role in the development of theory and algorithms of complementarity problems. In this paper, we establish sufficient conditions to ensure the strict feasibility of a nonlinear complementarity problem. Our analysis method, based on a newly introduced concept ..."
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Cited by 2 (0 self)
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The strict feasibility plays an important role in the development of theory and algorithms of complementarity problems. In this paper, we establish sufficient conditions to ensure the strict feasibility of a nonlinear complementarity problem. Our analysis method, based on a newly introduced concept
Results 1  10
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228