nonnegative polynomials

DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization

  • Amir Ali Ahmadi
  • Anirudha Majumdar
    • Categories Linear Programming, Second-Order Cone Programming, Semi-definite Programming Tags , , , , ,

    In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it can be applied. In this paper, we introduce DSOS and SDSOS optimization as linear programming and second-order cone … Read more

    Moment approximations for set-semidefinite polynomials

  • Peter J.C. Dickinson
  • Janez Povh
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    The set of polynomials which are nonnegative over a subset of the nonnegative orthant (we call them set semidefinite) have many uses in optimization. A common example of this type of set is the set of copositive matrices, where effectively we are considering nonnegativity over the entire nonnegative orthant and we limit the polynomials to … Read more