RECIPES FOR BUILDING THE DUAL OF CONIC OPTIMIZATION PROBLEM
Abstract: Building the dual of
the primal problem of Conic Optimization (CO) is a very important step to make
the flnding optimal solution. In many cases a given problem does not have the
simple structure of CO problem (i.e., minimizing a linear function over an
intersection between a–ne space and convex cones) but there are several conic
constraints and sometimes also equality constraints. In this paper we deal with
the question how to form the dual problem in such cases. We discuss theanswer
by considering several conic constraints with or without equality constraints. The
recipes for building the dual of such cases is formed in standard matrix forms,
such that it can be used easily on the numerical experiment. Special attention
isgiven to dual development of special classes of CO problems, i.e., conic
quadratic and semideflnite problems. In this paper, we also briefly present
some preliminaries theory on CO as an introduction to the main topic.
Author: D. Chaerani
Journal Code: jpmatematikagg100005
