Stochastic Programming

Direct search based on probabilistic feasible descent for bound and linearly constrained problems

  • Serge Gratton
  • Clément W. Royer
  • Luis Nunes Vicente
  • Z. Zhang
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Direct search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region and typically consist of positive generators of approximate tangent cones (which then … Read more

    Gas Storage Valuation in Incomplete Markets

  • Nils Löhndorf
  • David Wozabal
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , ,

    Natural gas storage valuation is an important problem in energy trading, yet most valuation approaches are based on heuristics or ignore that gas markets are incomplete. We propose an exact valuation model for incomplete gas markets based on multistage stochastic programming. Market incompleteness structurally changes the problem of storage valuation and asset backed trading and … Read more

    Optimized Bonferroni Approximations of Distributionally Robust Joint Chance Constraints

  • Shabbir Ahmed
  • Ruiwei Jiang
  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold $\epsilon$, over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to … Read more

    Scenario grouping and decomposition algorithms for chance-constrained programs

  • Shabbir Ahmed
  • Yan Deng
  • Huiwen Jia
  • Jon Lee
  • Siqian Shen
    • Categories Stochastic Programming

    A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, … Read more

    Decomposition Algorithms for Two-Stage Distributionally Robust Mixed Binary Programs

  • Manish Bansal
  • Kuo-Ling Huang
  • Sanjay Mehrotra
    • Categories 0-1 Programming, Robust Optimization, Stochastic Programming

    In this paper, we introduce and study a two-stage distributionally robust mixed binary problem (TSDR-MBP) where the random parameters follow the worst-case distribution belonging to an uncertainty set of probability distributions. We present a decomposition algorithm, which utilizes distribution separation procedure and parametric cuts within Benders’ algorithm or L-shaped method, to solve TSDR-MBPs with binary … Read more

    Optimization Techniques for Tree-Structured Nonlinear Problems

  • Jens Hübner
  • Martin Schmidt
  • Marc C. Steinbach
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , ,

    Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be … Read more

    Statistical Inference of Semidefinite Programming

  • Alexander Shapiro
    • Categories Semi-definite Programming, Stochastic Programming Tags , , , , , ,

    In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the `true’ covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we consider … Read more

    On Intersection of Two Mixing Sets with Applications to Joint Chance-Constrained Programs

  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Xiao Liu
    • Categories Integer Programming, Stochastic Programming

    We study the polyhedral structure of a generalization of a mixing set described by the intersection of two mixing sets with two shared continuous variables, where one continuous variable has a positive coefficient in one mixing set, and a negative coefficient in the other. Our developments are motivated from a key substructure of linear joint … Read more

    Risk-based Loan Pricing: Portfolio Optimization Approach With Marginal Risk Contribution

  • So Yeon Chun
  • Miguel A. Lejeune
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , , , ,

    We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrowers’ response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We … Read more

    Data-Driven Optimization of Reward-Risk Ratio Measures

  • Ran Ji
    • Categories Finance and Economics, Stochastic Programming Tags , , , , ,

    We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more