Exterior point algorithms for nearest points and convex quadratic programs

Exterior point algorithms for nearest points and convex quadratic programs

We consider the problem of finding the nearest point (by Euclidean distance) in a simplicial cone to a given point, and develop an exterior penalty algorithm for it. Each iteration in the algorithm consists of a single Newton step following a reduction in the value of the penalty parameter. Proofs of convergence of the algorithm are given. Various other versions of exterior penalty algorithms f...

A Primal-dual Interior Point Algorithm for Convex Quadratic Programs

In this paper, we propose a feasible primal-dual path-following algorithm for convex quadratic programs.At each interior-point iteration the algorithm uses a full-Newton step and a suitable proximity measure for tracing approximately the central path.We show that the short-step algorithm has the best known iteration bound,namely O( √ n log (n+1) ).

Convex Sets and Nearest Points. Ip

Primal-dual exterior point method for convex optimization

We introduce and study the primal-dual exterior point (PDEP) method for convex optimization problems. The PDEP is based on the Nonlinear Rescaling (NR) multipliers method with dynamic scaling parameters update. The NR method at each step alternates finding the unconstrained minimizer of the Lagrangian for the equivalent problem with both Lagrange multipliers and scaling parameters vectors updat...

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...