A new barrier for a class of semidefinite problems

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

Ariyawansa and Zhu [5] have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDP’s). SSDP’s may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLP’s). Zhao [25] has derived a decomposition algorithm for SLP’s based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Özevin [17] have exten...

New complexity analysis of a full Nesterov-Todd steps IIPM for semidefinite optimization

Primal-dual path-following algorithms for circular programming

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

A Method for Solving Convex Quadratic Programming Problems Based on Differential-algebraic equations

In this paper, a new model based on differential-algebraic equations(DAEs) for solving convex quadratic programming(CQP) problems is proposed. It is proved that the new approach is guaranteed to generate optimal solutions for this class of optimization problems. This paper also shows that the conventional interior point methods for solving (CQP) problems can be viewed as a special case of the n...