Infinite Dimensional Optimization

Semi-infinite linear programming approaches to semidefinite programming problems

  • Kartik Krishnan
  • John E. Mitchell
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    Interior point methods, the traditional methods for the $SDP$, are fairly limited in the sizes of problems they can handle. This paper deals with an $LP$ approach to overcome some of these shortcomings. We begin with a semi-infinite linear programming formulation of the $SDP$ and discuss the issue of its discretization in some detail. We … Read more

    On duality theory of conic linear problems

  • Alexander Shapiro
    • Categories Cone Programming, Convex Optimization, Infinite Dimensional Optimization

    In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate duality approach where the questions of “no duality … Read more