An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions

  • Radu Ioan Bot
  • Ernö Robert Csetnek
  • Szilard Csaba Laszlo
    • Categories Nonsmooth Optimization Tags , , , ,

    We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is … Read more

    Optimal scheduling for replacing perimeter guarding unmanned aerial vehicles

  • Oleg Burdakov
  • Patrick Doherty
  • Jonas Kvarnström
    • Categories Civil and Environmental Engineering, Global Optimization, Scheduling

    Guarding the perimeter of an area in order to detect potential intruders is an important task in a variety of security-related applications. This task can in many circumstances be performed by a set of camera-equipped unmanned aerial vehicles (UAVs). Such UAVs will occasionally require refueling or recharging, in which case they must temporarily be replaced … Read more

    Multi-stage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set

  • Dick den Hertog
  • Krzysztof Postek
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , , ,

    In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period … Read more

    Planar Maximum Coverage Location Problem with Partial Coverage and Rectangular Demand and Service Zones

  • Manish Bansal
  • Kiavash Kianfar
    • Categories Combinatorial Optimization

    We study the planar maximum coverage location problem (MCLP) with rectilinear distance and rectangular demand zones in the case where “partial coverage” is allowed in its true sense, i.e., when covering only part of a demand zone is allowed and the coverage accrued as a result of this is proportional to the demand of the … Read more

    Solving bilevel combinatorial optimization as bilinear min-max optimization via a branch-and-cut algorithm

  • Artur Alves Pessoa
  • Michael Poss
  • Marcos Costa Roboredo
    • Categories Branch and Cut Algorithms Tags , , ,

    In this paper, we propose a generic branch-and -cut algorithm for a special class of bi-level combinatorial optimization problems. Namely, we study such problems that can be reformulated as bilinear min-max combinatorial optimization problems. We show that the reformulation can be efficiently solved by a branch-and-cut algorithm whose cuts represent the inner maximization feasibility set. … Read more

    Douglas-Rachford splitting for nonconvex feasibility problems

  • Guoyin Li
  • Ting Kei Pong
    • Categories Nonsmooth Optimization

    We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the direct adaptation of the method … Read more

    Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex Optimization

    We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full fledged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to an objective function value) to one returned … Read more

    Randomized First-order Methods for Saddle Point Optimization

  • Cong D. Dang
  • Guanghui Lan
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is a direct product of many convex sets. Our algorithms can achieve ${\cal O}(1/N)$ rate of convergence by solving only one dual subproblem at each iteration. Our algorithms can also achieve ${\cal O}(1/N^2)$ rate of convergence if a … Read more

    A Proximal Multiplier Method for Convex Separable Symmetric Cone Optimization

  • Julio López
  • Erik Alex Papa Quiroz
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    This work is devoted to the study of a proximal decomposition algorithm for solving convex symmetric cone optimization with separable structures. The algorithm considered is based on the decomposition method proposed by Chen and Teboulle (1994), and the proximal generalized distance defined by Auslender and Teboulle (2006). Under suitable assumptions, first a class of proximal … Read more

    Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

  • Alvaro Lorca
  • Xu Andy Sun
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today’s power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. … Read more