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CSDP, a C library for semidefinite programming.
, 1997
"... this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. ..."
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Cited by 185 (1 self)
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this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. Finally, we present results from the solution of a number of test problems. 2 The SDP Problem We consider semidefinite programming problems of the form max tr (CX)
SEMIDEFINITE PROGRAMMING RELAXATIONS OF NONCONVEX PROBLEMS IN CONTROL AND COMBINATORIAL OPTIMIZATION
"... We point out some connections between applications of semidefinite programming in control and in combinatorial optimization. In both fields semidefinite programs arise as convex relaxations of NPhard quadratic optimization problems. We also show that these relaxations are readily extended to optimi ..."
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Cited by 18 (2 self)
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We point out some connections between applications of semidefinite programming in control and in combinatorial optimization. In both fields semidefinite programs arise as convex relaxations of NPhard quadratic optimization problems. We also show that these relaxations are readily extended to optimization problems over bilinear matrix inequalities.
Some Heuristics and Testproblems for Nonconvex Quadratic Programming over a Simplex
 Humboldt University Berlin
, 1998
"... Keywords:global optimization, nonconvex quadratic programming, heuristics, Bezier methods, test problems In this paper we compare two methods for estimating a global minimizer of an inde nite quadratic form over a simplex. The rst method is based on the enumeration of local minimizers of a socalled ..."
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Cited by 2 (1 self)
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Keywords:global optimization, nonconvex quadratic programming, heuristics, Bezier methods, test problems In this paper we compare two methods for estimating a global minimizer of an inde nite quadratic form over a simplex. The rst method is based on the enumeration of local minimizers of a socalled control polytope. The second method is based on an approximation of the convex envelope using semide nite programming. In order to test the algorithms a method for generating random test problems is presented where the optimal solution is known and the number of binding constraints is prescribed. Moreover, it is investigated if some modi cations of the objective function in uence the performance of the algorithms. Numerical experiments are reported. 1
Polynomial primaldual cone affine scaling for semidefinite programming
, 1996
"... In this paper we generalize the primaldual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared t ..."
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Cited by 2 (0 self)
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In this paper we generalize the primaldual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared to other primaldual affine scaling algorithms for semidefinite programming (see, De Klerk, Roos and Terlaky [3]), our algorithm enjoys the lowest computational complexity.
Topological Fixture Synthesis Using Semidefinite Programming
, 1999
"... Topological fixture synthesis is an important issue to consider for most manufacturing operations performed on solid and sheet metal workpieces. Recentwork on optimal fixture design has focused on determining the positions of locators and clamps to minimize workpiece deformation. These approaches re ..."
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Topological fixture synthesis is an important issue to consider for most manufacturing operations performed on solid and sheet metal workpieces. Recentwork on optimal fixture design has focused on determining the positions of locators and clamps to minimize workpiece deformation. These approaches restrict the locators and clamps to three mutually perpendicular planes selected according to the "321" or the "N21" locating principle. In this article, mixedinteger quadratic programming is used to identify the optimal distribution and position (i.e., topology) of locators in order to minimize the mean compliance of the workpiece. We present a semidefinite programming (SDP) relaxation method to solve the underlying combinatorial problem. Illustrative examples (with symmetric and asymmetric loads) validate the formulation and solution approach.