stochastic

A Sequential Quadratic Programming Method for Optimization with Stochastic Objective Functions, Deterministic Inequality Constraints and Robust Subproblems

  • Songqiang Qiu
  • Vyacheslav Kungurtsev
    • Categories Constrained Nonlinear Optimization, Other Topics, Stochastic Programming Tags , , ,

    In this paper, a robust sequential quadratic programming method of Burke and Han (Math Programming, 1989)  for constrained optimization is generalized to problem with stochastic objective function, deterministic equality and inequality constraints. A stochastic line search scheme in Paquette and Scheinberg (SIOPT, 2020) is employed to globalize the steps. We show that in the case … Read more

    Optimization of noisy blackboxes with adaptive precision

  • Stéphane Alarie
  • Charles Audet
  • Pierre-Yves Bouchet
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization Tags , , , , , , ,

    In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors. Sometimes, the source of these errors is identified and controllable, in the sense that it is possible to … Read more

    Robust stochastic optimization with the proximal point method

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. In this work, we show that a wide class of such algorithms on strongly convex problems can be augmented with sub-exponential confidence bounds at an overhead cost that is only … Read more

    Stochastic model-based minimization of weakly convex functions

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    We consider an algorithm that successively samples and minimizes stochastic models of the objective function. We show that under weak-convexity and Lipschitz conditions, the algorithm drives the expected norm of the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. Our result yields the first complexity guarantees for the stochastic proximal point algorithm … Read more

    Stochastic subgradient method converges at the rate (k^{-1/4})$ on weakly convex function

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Nonsmooth Optimization Tags , ,

    We prove that the projected stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. Article Download View Stochastic subgradient method converges at the rate (k^{-1/4})$ on weakly convex function

    A deterministic algorithm for solving multistage stochastic programming problems

  • Regan Baucke
  • Anthony Downward
  • Golbon Zakeri
    • Categories Stochastic Programming Tags , , , ,

    Multistage stochastic programming problems are an important class of optimisation problems, especially in energy planning and scheduling. These problems and their solution methods have been of particular interest to researchers in stochastic programming recently. Because of the large scenario trees that these problems induce, current solution methods require random sampling of the tree in order … Read more

    A new Search via Probability Algorithm for solving Engineering Optimization Problems

  • Nguyen Huu Thong
    • Categories Applications - Science and Engineering, Global Optimization, Stochastic Programming Tags , , ,

    The Search Algorithms have been introduced in the paper [3][6] under the name ‘Search via Probability Algorithm’. These optimization techniques converge very fast and are very efficient for solving optimization problems with very large scale feasible domains. But these optimization techniques are not effective in solving the numerical optimization problems with long narrow feasible domains. … Read more

    A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

  • Tran Van Hao
  • Nguyen Huu Thong
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Stochastic Approaches Tags , , ,

    This paper proposes a new probabilistic algorithm for solving multi-objective optimization problems – Probability-Driven Search Algorithm. The algorithm uses probabilities to control the process in search of Pareto optimal solutions. Especially, we use the absorbing Markov Chain to argue the convergence of the algorithm. We test this approach by implementing the algorithm on some benchmark … Read more

    Approximate Dynamic Programming with Bezier Curves/Surfaces for Top-percentile traffic routing

  • Andreas Grothey
  • Xinan Yang
    • Categories Dynamic Programming, Telecommunications Tags , , , , ,

    Multi-homing is used by Internet Service Provider (ISP) to connect to the Internet via different network providers. This study investigates the optimal routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the $\theta$-th highest volume of traffic shipped). We call this problem the Top-percentile Traffic … Read more

    On-Line Economic Optimization of Energy Systems Using Weather Forecast Information

  • Mihai Anitescu
  • Emil M. Constantinescu
  • Victor M. Zavala
  • Theodore Krause
    • Categories Chemical Engineering, Control Applications, Stochastic Programming Tags , , , , ,

    We establish an on-line optimization framework to exploit weather forecast information in the operation of energy systems. We argue that anticipating the weather conditions can lead to more proactive and cost-effective operations. The framework is based on the solution of a stochastic dynamic real-time optimization (D-RTO) problem incorporating forecasts generated from a state-of-the-art weather prediction … Read more