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Exact Solution Approaches for Integer Linear Generalized Maximum Multiplicative Programs Through the Lens of Multi-objective Optimization

  • Hadi Charkhgard
  • Payman Ghasemi Saghand
    • Categories Applications - OR and Management Sciences, Game Theory, Integer Programming Tags , , , ,

    We study a class of single-objective nonlinear optimization problems, the so-called Integer Linear Generalized Maximum Multiplicative Programs (IL-GMMP). This class of optimization problems has a significant number of applications in different fields of study including but not limited to game theory, systems reliability, and conservative planning. An IL-GMMP can be reformulated as a mixed integer … Read more

    Stochastic Optimization Models of Insurance Mathematics

  • Yuri M. Ermoliev
  • Bogdan V. Norkin
  • Vladimir I. Norkin
    • Categories Finance and Economics, Multi-Criteria Optimization, Stochastic Programming Tags , , , , , , , , ,

    The paper overviews stochastic optimization models of insurance mathematics and methods for their solution from the point of view of stochastic programming and stochastic optimal control methodology, with vector optimality criteria. The evolution of an insurance company’s capital is considered in discrete time. The main random variables, which influence this evolution, are levels of payments, … Read more

    BiLQ: An Iterative Method for Nonsymmetric Linear Systems with a Quasi-Minimum Error Property

  • Alexis Montoison
  • Dominique Orban
    • Categories Other Topics Tags , , , , , , ,

    We introduce an iterative method named BiLQ for solving general square linear systems Ax = b based on the Lanczos biorthogonalization process defined by least-norm subproblems, and is a natural companion to BiCG and QMR. Whereas the BiCG (Fletcher, 1976), CGS (Sonneveld, 1989) and BiCGSTAB (van der Vorst, 1992) iterates may not exist when the … Read more

    Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates

  • Charles Audet
  • Kwassi Joseph Dzahini
  • Michael Kokkolaras
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization, Other Topics, Unconstrained Optimization Tags , , , ,

    We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based … Read more

    Objective Selection for Cancer Treatment: An Inverse Optimization Approach

  • Temitayo Ajayi
  • Andrew J. Schaefer
  • Taewoo Lee
    • Categories Biomedical Applications, Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , , , ,

    In radiation therapy treatment-plan optimization, selecting a set of clinical objectives that are tractable and parsimonious yet effective is a challenging task. In clinical practice, this is typically done by trial and error based on the treatment planner’s subjective assessment, which often makes the planning process inefficient and inconsistent. We develop the objective selection problem … Read more

    Risk-Averse Optimal Control

  • Alois Pichler
  • Ruben Schlottter
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    In the context of multistage stochastic optimization, it is natural to consider nested risk measures, which originate by repeatedly composing risk measures, conditioned on realized observations. Starting from this discrete time setting, we extend the notion of nested risk measures to continuous time by adapting the risk levels in a time dependent manner. This time … Read more

    Representation of the Pareto front for heterogeneous multi-objective optimization

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    Optimization problems with multiple objectives which are expensive, i.e. where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance analytically given, this can be used in … Read more

    On the intrinsic core of convex cones in real linear spaces

  • Ali P. Farajzadeh
  • Christian Günther
  • Christiane Tammer
  • Bahareh Khazayel
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , , , , , ,

    Convex cones play an important role in nonlinear analysis and optimization theory. In particular, specific normal cones and tangent cones are known to be convex cones, and it is a crucial fact that they are useful geometric objects for describing optimality conditions. As important applications (especially, in the fields of optimal control with PDE constraints, … Read more

    Computational Enhancement in the Application of the Branch and Bound Method for Linear Integer Programs and Related Models

  • Ali Al-Hasani
  • Andrew C. Eberhard
  • Masar Al-Rabeeah
  • Santosh Kumar
  • Elias Munapo
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

    In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations … Read more

    Methods for multiobjective bilevel optimization

  • Gabriele Eichfelder
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    This paper is on multiobjective bilevel optimization, i.e. on bilevel optimization problems with multiple objectives on the lower or on the upper level, or even on both levels. We give an overview on the major optimality notions used in multiobjective optimization. We provide characterization results for the set of optimal solutions of multiobjective optimization problems … Read more