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22
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
, 1998
"... SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This pape ..."
Abstract

Cited by 1368 (5 self)
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SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This paper describes how to work with this toolbox.
SDPT3  a MATLAB software package for semidefinite programming
 OPTIMIZATION METHODS AND SOFTWARE
, 1999
"... This software package is a Matlab implementation of infeasible pathfollowing algorithms for solving standard semidefinite programming (SDP) problems. Mehrotratype predictorcorrector variants are included. Analogous algorithms for the homogeneous formulation of the standard SDP problem are also imp ..."
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Cited by 361 (16 self)
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This software package is a Matlab implementation of infeasible pathfollowing algorithms for solving standard semidefinite programming (SDP) problems. Mehrotratype predictorcorrector variants are included. Analogous algorithms for the homogeneous formulation of the standard SDP problem are also implemented. Four types of search directions are available, namely, the AHO, HKM, NT, and GT directions. A few classes of SDP problems are included as well. Numerical results for these classes show that our algorithms are fairly efficient and robust on problems with dimensions of the order of a few hundreds.
Using SeDuMi 1.0x , A Matlab TOOLBOX FOR OPTIMIZATION OVER SYMMETRIC CONES
, 1999
"... SeDuMi is an addon for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This p ..."
Abstract

Cited by 46 (0 self)
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SeDuMi is an addon for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This paper describes how to work with this toolbox.
Implementation of interior point methods for mixed semidefinite and second order cone optimization problems
 Optimization Methods and Software
"... There is a large number of implementational choices to be made for the primaldual interior point method in the context of mixed semidefinite and second order cone optimization. This paper presents such implementational issues in a unified framework, and compares the choices made by different resear ..."
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Cited by 41 (0 self)
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There is a large number of implementational choices to be made for the primaldual interior point method in the context of mixed semidefinite and second order cone optimization. This paper presents such implementational issues in a unified framework, and compares the choices made by different research groups. This is also the first paper to provide an elaborate discussion of the implementation in SeDuMi.
InfeasibleStart PrimalDual Methods And Infeasibility Detectors For Nonlinear Programming Problems
 Mathematical Programming
, 1996
"... In this paper we present several "infeasiblestart" pathfollowing and potentialreduction primaldual interiorpoint methods for nonlinear conic problems. These methods try to find a recession direction of the feasible set of a selfdual homogeneous primaldual problem. The methods under ..."
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Cited by 38 (6 self)
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In this paper we present several "infeasiblestart" pathfollowing and potentialreduction primaldual interiorpoint methods for nonlinear conic problems. These methods try to find a recession direction of the feasible set of a selfdual homogeneous primaldual problem. The methods under consideration generate an fflsolution for an fflperturbation of an initial strictly (primal and dual) feasible problem in O( p ln fflae f ) iterations, where is the parameter of a selfconcordant barrier for the cone, ffl is a relative accuracy and ae f is a feasibility measure. We also discuss the behavior of pathfollowing methods as applied to infeasible problems. We prove that strict infeasibility (primal or dual) can be detected in O( p ln ae \Delta ) iterations, where ae \Delta is a primal or dual infeasibility measure. 1 Introduction Nesterov and Nemirovskii [9] first developed and investigated extensions of several classes of interiorpoint algorithms for linear programming t...
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
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On Two InteriorPoint Mappings for Nonlinear Semidefinite Complementarity Problems
 Mathematics of Operations Research
, 1997
"... Extending our previous work Monteiro and Pang (1996), this paper studies properties of two fundamental mappings associated with the family of interiorpoint methods for solving monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. The first of these m ..."
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Cited by 27 (9 self)
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Extending our previous work Monteiro and Pang (1996), this paper studies properties of two fundamental mappings associated with the family of interiorpoint methods for solving monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. The first of these maps lead to a family of new continuous trajectories which include the central trajectory as a special case. These trajectories completely "fill up" the set of interior feasible points of the problem in the same way as the weighted central paths do the interior of the feasible region of a linear program. Unlike the approach based on the theory of maximal monotone maps taken by Shida and Shindoh (1996) and Shida, Shindoh, and Kojima (1995), our approach is based on the theory of local homeomorphic maps in nonlinear analysis. Key words: interior point methods, mixed nonlinear complementarity problems, generalized complementarity problems, maximal monotonicity, monotone mappings, continuous traj...
Duality Results For Conic Convex Programming
, 1997
"... This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone infinite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are give ..."
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Cited by 26 (10 self)
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This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone infinite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include GordonStiemke type theorems, Farkas type theorems, perfect duality, Slater condition, regularization, Ramana's duality, and approximate dualities. The dual representations of various convex sets, convex cones and conic convex programs are also discussed.
Conic convex programming and selfdual embedding.
 Optimization Methods and Software,
, 2000
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On Weighted Centers For Semidefinite Programming
, 1996
"... In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the vspace framework, which is purely based on the symmetric primaldual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weigh ..."
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Cited by 19 (6 self)
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In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the vspace framework, which is purely based on the symmetric primaldual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weighted centers. Relations with other primaldual maps are discussed. Key words. semidefinite programming, symmetric primaldual transformation, weighted center. 1 Econometric Institute, Erasmus University Rotterdam, The Netherlands, sturm@few.eur.nl. 2 Econometric Institute, Erasmus University Rotterdam, The Netherlands, zhang@few.eur.nl Sturm and Zhang: On weighted centers for SDP 1 1. Introduction The central path plays a fundamental role in the interior point methodology, both for linear and semidefinite programming. Megiddo [10] showed some highly interesting properties of the central path for linear programming. The fact that ¯centers are the minimizers of the logarithmic barrier f...