spectral bundle

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

    A Linear Programming Approach to Semidefinite Programming Problems

  • Kartik Krishnan
  • John E. Mitchell
    • Categories Combinatorial Optimization, Linear Programming, Semi-definite Programming Tags , , , , ,

    Until recently, the study of interior point methods has dominated algorithmic research in semidefinite programming (SDP). From a theoretical point of view, these interior point methods offer everything one can hope for; they apply to all SDP’s, exploit second order information and offer polynomial time complexity. Still for practical applications with many constraints $k$, the … Read more