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Second-order cone programming
TLDR
Second-order cone programming (SOCP) problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the Cartesian product of second order (Lorentz) cones. Expand
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Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
  • F. Alizadeh
  • Mathematics, Computer Science
  • SIAM J. Optim.
  • 1 February 1995
TLDR
This paper studies the semidefinite programming SDP problem, i.e., the optimization problem of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semideFinite. Expand
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Extension of primal-dual interior point algorithms to symmetric cones
TLDR
We show that the so-called commutative class of primal-dual interior point algorithms which were designed by Monteiro and Zhang for semidefinite programming extends word-for-word to optimization problems over all symmetric cones. Expand
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Complementarity and nondegeneracy in semidefinite programming
TLDR
Primal and dual nondegeneracy conditions are defined for semidefinite programming. Expand
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Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results
Primal-dual interior-point path-following methods for semidefinite programming are considered. Several variants are discussed, based on Newton's method applied to three equations: primal feasibility,Expand
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Physical mapping of chromosomes using unique probes
TLDR
The goal of physical mapping of the genome is to reconstruct a strand of DNA given a collection of overlapping fragments, or clones, from the strand. Expand
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A New Primal-Dual Interior-Point Method for Semidefinite Programming
The semidefinite programming problem (SDP) is: min tr CX s.t. tr A{sub i}X = b{sub i}, i = 1, {hor_ellipsis}, m, and X {>=} 0. Here C and A{sub i} are fixed symmetric matrices and X {>=} 0 is aExpand
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Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones
TLDR
We present a general framework whereby analysis of interior-point algorithms for semidefinite programming can be extended verbatim to optimization problems over all classes of symmetric cones derivable from associative algebras. Expand
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Combinatorial Optimization with Semi-Definite Matrices
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Physical mapping of chromosomes: A combinatorial problem in molecular biology
TLDR
This paper is concerned wth the physical mapping of DNA molecules using data about the hybridization of oligonucleotide probes to a library of clones. Expand
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