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Solving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivatives
In this paper, we introduce transformations that convert a large class of linear and/or nonlinear semidefinite programming (SDP) problems into nonlinear optimization problems over "orthants" of the form (R^n)++ × R^N, ...
A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs
The authors of this paper recently introduced a transformation that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation ...
Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation
Recently, the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix function of a certain form into the positivity constraint on n scalar variables ...
Maximum Stable Set Formulations and Heuristics Based on Continuous Optimization
The stability number for a given graph G is the size of a maximum stable set in G. The Lovasz theta number provides an upper bound on the stability number and can be computed as the optimal value of the Lovasz semidefinite ...
Rank-Two Relaxation Heuristics for Max-Cut and Other Binary Quadratic Programs
Semidefinite relaxation for certain discrete optimization problems involves replacing a vector-valued variable by a matrix-valued one, producing a convex program while increasing the number of variables by an order of ...