Mehdi Karimi

Domain-Driven Solver (DDS): a MATLAB-based Software Package for Convex Optimization Problems in Domain-Driven Form

  • Mehdi Karimi
  • Levent Tunçel
    • Categories Convex and Nonsmooth Optimization, Optimization Software and Modeling Systems Tags , , , ,

    Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [11]. The current version of DDS accepts every combination of the following function/set constraints: (1) symmetric cones (LP, SOCP, and SDP); (2) quadratic constraints; (3) direct sums of an arbitrary collection of 2-dimensional convex sets defined as the epigraphs of … Read more

    Status Determination by Interior-Point Methods for Convex Optimization Problems in Domain-Driven Form

  • Mehdi Karimi
  • Levent Tunçel
    • Categories Convex Optimization Tags , , , ,

    We study the geometry of convex optimization problems given in a Domain-Driven form and categorize possible statuses of these problems using duality theory. Our duality theory for the Domain-Driven form, which accepts both conic and non-conic constraints, lets us determine and certify statuses of a problem as rigorously as the best approaches for conic formulations … Read more

    Primal-Dual Interior-Point Methods for Domain-Driven Formulations: Algorithms

  • Mehdi Karimi
  • Levent Tunçel
    • Categories Convex Optimization Tags , , ,

    We study infeasible-start primal-dual interior-point methods for convex optimization problems given in a typically natural form we denote as Domain-Driven formulation. Our algorithms extend many advantages of primal-dual interior-point techniques available for conic formulations, such as the current best complexity bounds, and more robust certificates of approximate optimality, unboundedness, and infeasibility, to Domain-Driven formulations. The … Read more

    Primal-Dual Entropy Based Interior-Point Algorithms for Linear Optimization

  • Mehdi Karimi
  • Shen Luo
  • Levent Tunçel
    • Categories Linear Programming

    We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector algorithm together with a homogeneous self-dual embedding, we can achieve the current best iteration complexity bound for linear optimization. … Read more

    An Improvised Approach to Robustness in Linear Optimization

  • Mehdi Karimi
  • Somayeh Moazeni
  • Levent Tunçel
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags ,

    We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. In addition to many practical advantages, due to the flexibility of our approach, we are able to prove that the robust optimal solutions generated by our algorithms are at least as desirable … Read more