Stochastic Programming

Bounds on Risk-averse Mixed-integer Multi-stage Stochastic Programming Problems with Mean-CVaR

  • M. Selim Akturk
  • Özlem Cavus
  • Ali Irfan Mahmutogullari
    • Categories Stochastic Programming

    Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions and the objective function is a dynamic measure of risk. For this reason, we propose a scenario tree decomposition approach, namely group subproblem approach, … Read more

    Parallel stochastic line search methods with feedback for minimizing finite sums

  • Dragana Bajović
  • Dušan Jakovetić
  • Nataša Krejić
  • Nataša Krklec Jerinkić
    • Categories Global Optimization, Stochastic Programming

    We consider unconstrained minimization of a finite sum of $N$ continuously differentiable, not necessarily convex, cost functions. Several gradient-like (and more generally, line search) methods, where the full gradient (the sum of $N$ component costs’ gradients) at each iteration~$k$ is replaced with an inexpensive approximation based on a sub-sample~$\mathcal N_k$ of the component costs’ gradients, … Read more

    Guaranteed Bounds for General Non-discrete Multistage Risk-Averse Stochastic Optimization Programs

  • Francesca Maggioni
  • Georg Ch. Pflug
    • Categories Stochastic Programming Tags , , , , ,

    In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such ”infinite” problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e. finite … Read more

    Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

  • Byung-Geun Choi
  • Ruiwei Jiang
  • Napat Rujeerapaiboon
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , ,

    Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more

    Optimization Methods for Large-Scale Machine Learning

  • Léon Bottou
  • Frank E. Curtis
  • Jorge Nocedal
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of … Read more

    Decomposability and time consistency of risk averse multistage programs

  • Alexander Shapiro
  • Kerem Ugurlu
    • Categories Stochastic Programming Tags , ,

    Two approaches to time consistency of risk averse multistage stochastic problems were dis- cussed in the recent literature. In one approach certain properties of the corresponding risk measure are postulated which imply its decomposability. The other approach deals directly with conditional optimality of solutions of the considered problem. The aim of this paper is to … Read more

    Pricing wind: a revenue adequate, cost recovering uniform auction for electricity markets with intermittent generation

  • Endre Bjorndal
  • Mette Bjorndal
  • Geoff Pritchard
  • Golbon Zakeri
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    With greater penetration of renewable generation, the uncertainty faced in electricity markets has increased substantially. Conventionally, generators are assigned a pre-dispatch quantity in advance of real time, based on estimates of uncertain quantities. Expensive real time adjustments then need to be made to ensure demand is met, as uncertainty takes on a realization. We propose … Read more

    Path Constraints in Tychastic and Unscented Optimal Control: Theory, Applications and Experimental Results

  • M. Karpenko
  • Isaac Ross
  • R. J. Proulx
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , ,

    In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties … Read more

    SCORE Allocations for Bi-objective Ranking and Selection

  • Guy Feldman
  • Susan R. Hunter
    • Categories Global Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , ,

    The bi-objective R&S problem is a special case of the multi-objective simulation optimization problem in which two conflicting objectives are known only through dependent Monte Carlo estimators, the decision space or number of systems is finite, and each system can be sampled to some extent. The solution to the bi-objective R&S problem is a set … Read more

    A CVaR Scenario-based Framework: Minimizing Downside Risk of Multi-asset Class Portfolios

  • Kartik Krishnan Sivaramakrishnan
  • Robert Stamicar
    • Categories Applications - OR and Management Sciences, Finance and Economics, Stochastic Programming Tags , ,

    Multi-asset class (MAC) portfolios can be comprised of investments in equities, fixed-income, commodities, foreign-exchange, credit, derivatives, and alternatives such as real-estate and private equity. The return for such {\em non-linear} portfolios is {\em asymmetric} with significant tail risk. The traditional Markowitz Mean-Variance Optimization (MVO) framework, that linearizes all the assets in the portfolio and uses … Read more