Newly, there has been significant research interest in the exact solution of the AC optimal power flow (ACOPF) problem. A semideflnite relaxation solves many OPF problems globally. However, the real problem exists in which the semidefinite relaxation fails to yield the global solution. The appropriation of relaxation for ACOPF depends on the success or unfulflllment of the SDP relaxation. This paper demonstrates a quadratic ACOPF problem with a single negative eigenvalue in objective function subject to linear and conic constraints. The proposed solution method for ACOPF model covers the classical AC economic dispatch problem that is known to be NPhard.more »
This content will become publicly available on January 1, 2023
Alfonso: Matlab Package for Nonsymmetric Conic Optimization
We present alfonso, an opensource Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method of Skajaa and Ye. It enables optimization over any convex cone as long as a logarithmically homogeneous selfconcordant barrier is available for the cone or its dual. This includes many nonsymmetric cones, for example, hyperbolicity cones and their duals (such as sumofsquares cones), semidefinite and secondorder cone representable cones, power cones, and the exponential cone. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, algorithms for nonsymmetric conic optimization also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. The worstcase iteration complexity of alfonso is the best known for nonsymmetric cone optimization: [Formula: see text] iterations to reach an εoptimal solution, where ν is the barrier parameter of the barrier function used in the optimization. Alfonso can be interfaced with a Matlab function (supplied by the user) that computes the Hessian of a barrier function for the cone. A simplified interface is more »
 Publication Date:
 NSFPAR ID:
 10326038
 Journal Name:
 INFORMS Journal on Computing
 Volume:
 34
 Issue:
 1
 Page Range or eLocationID:
 11 to 19
 ISSN:
 10919856
 Sponsoring Org:
 National Science Foundation
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