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Second-order cone programming
TLDR
SOCP formulations are given for four examples: the convex quadratically constrained quadratic programming (QCQP) problem, problems involving fractional quadRatic functions, and many of the problems presented in the survey paper of Vandenberghe and Boyd as examples of SDPs can in fact be formulated as SOCPs and should be solved as such.
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
  • F. Alizadeh
  • Mathematics, Computer Science
    SIAM J. Optim.
  • 1 February 1995
TLDR
It is argued that many known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity carrying over in a similar fashion.
Extension of primal-dual interior point algorithms to symmetric cones
Abstract. In this paper 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
Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results
TLDR
The XZ+ZX method is more robust with respect to its ability to step close to the boundary, converges more rapidly, and achieves higher accuracy than other methods considered, including Mehrotra predictor-corrector variants and issues of numerical stability.
Complementarity and nondegeneracy in semidefinite programming
TLDR
It is shown that primal and dual nondegeneracy and strict complementarity all hold generically and Numerical experiments suggest probability distributions for the ranks ofX andZ which are consistent with the nondEGeneracy conditions.
Physical mapping of chromosomes using unique probes
TLDR
This work presents several algorithms to infer how the clones overlap, given data about each clone, in data used to map human chromosomes 21 and Y, in which relatively short substrings, or probes, are extracted from the ends of clones.
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 a
Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones
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
Physical mapping of chromosomes: A combinatorial problem in molecular biology
TLDR
Combinatorial algorithms are presented for solving approximations to the physical mapping of DNA molecules using data about the hybridization of oligonucleotide probes to a library of clones.
Optimization with Semidefinite, Quadratic and Linear Constraints
We consider optimization problems where variables have either linear, or convex quadratic or semideenite constraints. First, we deene and characterize primal and dual nondegeneracy and strict
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