A rounding procedure for semidefinite optimization

Recently, Mohammad-Nezhad and Terlaky studied the identification of the optimal partition for semidefinite optimization. An approximation of the optimal partition was obtained from a bounded sequence of solutions on, or in a neighborhood of the central path. Here, we use the approximation of the optimal partition in a rounding procedure to generate an approximate maximally … Read more

Generalized Support Set Invariancy Sensitivity Analysis

Support set invariancy sensitivity analysis deals with finding the range of the parameter variation where there are optimal solutions with the same positive variables for all parameter values throughout this range. This approach to sensitivity analysis has been studied for Linear Optimization (LO) and Convex Quadratic Optimization (CQO) problems, when they are in standard form. … Read more

Sensitivity analysis in convex quadratic optimization: simultaneous perturbation of the objective and right-hand-side vectors

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval … Read more

Sensitivity analysis in linear optimization: Invariant support set intervals

Sensitivity analysis is one of the most nteresting and preoccupying areas in optimization. Many attempts are made to investigate the problem’s behavior when the input data changes. Usually variation occurs in the right hand side of the constraints and/or the objective function coefficients. Degeneracy of optimal solutions causes considerable difficulties in sensitivity analysis. In this … Read more

Unifying optimal partition approach to sensitivity analysis in conic optimization

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as a function of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the … Read more