Abstract

In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic structure that is connected to SOCP. This algebra is a special case of a Euclidean Jordan algebra. After presenting duality theory, complementary slackness conditions, and definitions and algebraic characterizations of primal and dual nondegeneracy and strict complementarity we review the logarithmic barrier function for the SOCP problem and survey the path-following interior point algorithms for it. Next we examine numerically stable methods for solving the interior point methods and study ways that sparsity in the input data can be exploited. Finally we give some current and future research direction in SOCP.

Citations