A homogeneous interior-point algorithm for nonsymmetric convex conic optimization

A homogeneous interior-point algorithm for nonsymmetric convex conic optimization

A homogeneous infeasible-start interior-point algorithm for solving nonsymmetric convex conic optimization problems is presented. Starting each iteration from the vicinity of the central path, the method steps in the approximate tangent direction and then applies a correction phase to locate the next well-centered primal-dual point. Features of the algorithm include that it makes use only of th...

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...

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) function nor logarithmic barrier ...

Topics in Convex Optimization: Interior-point Methods, Conic Duality and Approximations

Generalization of Primal-Dual Interior-Point Methods to Convex Optimization Problems in Conic Form

We generalize primal-dual interior-point methods for linear programming problems to the convex optimization problems in conic form. Previously, the most comprehensive theory of symmetric primal-dual interior-point algorithms was given by Nesterov and Todd 8, 9] for the feasible regions expressed as the intersection of a symmetric cone with an aane subspace. In our setting, we allow an arbitrary...