Infinite Dimensional Optimization

A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization

  • Sanjay Mehrotra
  • Dávid Papp
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming Tags , , , , , , ,

    We first present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with non-differentiable semi-infinite … Read more

    A branch and bound approach for convex semi-infinite programming

  • Le Thi Hoai An
  • Mohand Ouanes
  • A. Ismael F. Vaz
    • Categories Convex Optimization, Semi-infinite Programming

    In this paper we propose an efficient approach for globally solving a class of convex semi-infinite programming (SIP) problems. Under the objective function and constraints (w.r.t. the variables to be optimized) convexity assumption, and appropriate differentiability, we propose a branch and bound exchange type method for SIP. To compute a feasible point for a SIP … Read more

    On the sufficiency of finite support duals in semi-infinite linear programming

  • Amitabh Basu
  • Kipp Martin
  • Christopher Thomas Ryan
    • Categories Semi-infinite Programming Tags ,

    We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show the finite support (Haar) dual is equivalent to the algebraic Lagrangian dual of the linear program. This settles a question left open by Anderson and Nash~\cite{anderson-nash}. … Read more

    Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming

  • Amitabh Basu
  • Kipp Martin
  • Christopher Thomas Ryan
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Semi-infinite Programming Tags , , , ,

    Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. We extend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations of important properties for primal-dual pairs of semi-infinite programs such as zero duality gap, feasibility, boundedness, and solvability. … Read more

    Calmness modulus of linear semi-infinite programs

  • M.J. Cánovas
  • Alexander Y. Kruger
  • Marco A. López
  • J. Parra
  • Michel Thera
    • Categories Linear Programming, Semi-infinite Programming Tags , , , ,

    Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide … Read more

    The Slater condition is generic in linear conic programming

  • Mirjam Dür
  • Georg Still
  • Bolor Jargalsaikhan
    • Categories Linear, Cone and Semidefinite Programming, Semi-infinite Programming

    We call a property generic if it holds for almost all problem instances. For linear conic problems, it has been shown in the literature that properties like uniqueness, strict complementarity or nondegeneracy of the optimal solution are generic under the assumption that Slater’s condition is fulfilled. The possibility that Slater’s condition generically fails has not … Read more

    Rate analysis of inexact dual first order methods: Application to distributed MPC for network systems

  • Ion Necoara
  • Valentin Nedelcu
    • Categories Convex Optimization, Distributed Control, Parallel Algorithms Tags , , , , ,

    In this paper we propose two dual decomposition methods based on inexact dual gradient information for solving large-scale smooth convex optimization problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first order methods based on approximate gradients and we prove sublinear rate of convergence … Read more

    A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

  • William Haskell
  • Alejandro Toriello
  • Michael Poremba
    • Categories Dynamic Programming, Semi-infinite Programming, Transportation Tags , , ,

    We propose a dynamic traveling salesman problem (TSP) with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which a decision’s cost is known only probabilistically beforehand but is revealed dynamically before the decision is executed. We formulate the problem as a dynamic program (DP) and compare it to static counterparts to … Read more

    POST-PARETO ANALYSIS FOR MULTIOBJECTIVE PARABOLIC CONTROL SYSTEMS

  • Henri Bonnel
    • Categories Distributed Control, Multi-Criteria Optimization Tags , , , ,

    In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is … Read more

    Data-driven Chance Constrained Stochastic Program

  • Yongpei Guan
  • Ruiwei Jiang
    • Categories Semi-definite Programming, Semi-infinite Programming, Stochastic Programming

    Chance constrained programming is an effective and convenient approach to control risk in decision making under uncertainty. However, due to unknown probability distributions of random parameters, the solution obtained from a chance constrained optimization problem can be biased. In practice, instead of knowing the true distribution of a random parameter, only a series of historical … Read more