Stochastic Programming

A Semi-Infinite Programming Approach for Distributionally Robust Reward-Risk Ratio Optimization with Matrix Moments Constraints

  • Yongchao Liu
  • Rudabeh Meskarian
  • Huifu Xu
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Reward-risk ratio optimization is an important mathematical approach in finance. In this paper, we revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken against the risk arising from ambiguity of the true distribution. We propose … Read more

    The impact of wind uncertainty on the strategic valuation of distributed electricity storage

  • Pedro Crespo Del Granado
  • Zhan Pang
  • Stein W. Wallace
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

    The intermittent nature of wind energy generation has introduced a new degree of uncertainty to the tactical planning of energy systems. Short-term energy balancing decisions are no longer (fully) known, and it is this lack of knowledge that causes the need for strategic thinking. But despite this observation, strategic models are rarely set in an … Read more

    Safe Approximations of Chance Constraints Using Historical Data

  • Dick den Hertog
  • Ihsan Yanıkoğlu
    • Categories Robust Optimization, Stochastic Programming

    This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, … Read more

    A Composite Risk Measure Framework for Decision Making under Uncertainty

  • Pengyu Qian
  • Zaiwen Wen
  • Zizhuo Wang
    • Categories Robust Optimization, Stochastic Programming

    In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution of uncertain model parameters, and the outer risk measure quantifies the risk that occurs when estimating … Read more

    Obtaining Lower Bounds from the Progressive Hedging Algorithm for Stochastic Mixed-Integer Programs

  • Dinakar Gade
  • Jean-Paul Watson
  • Gabriel Hackebeil
  • Sarah M. Ryan
  • Roger J.B. Wets
  • David L. Woodruff
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming

    We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using … Read more

    Stochastic Real-Time Scheduling of Wind-thermal Generation Units in an Electric Utility

  • Andrew Keane
  • Alireza Soroudi
  • Abbas Rabiee
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Stochastic Programming Tags , ,

    The objective of dynamic economic dispatch (DED) problem is to find the optimal dispatch of generation units in a given operation horizon to supply a pre-specified demand, while satisfying a set of constraints. In this paper, an efficient method based on Optimality Condition Decomposition (OCD) technique is proposed to solve the DED problem in real-time … Read more

    Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning

  • Shabbir Ahmed
  • Xu Andy Sun
  • Jikai Zou
    • Categories Stochastic Programming Tags , ,

    Electric Power Generation Expansion Planning (GEP) is the problem of determining an optimal construction and generation plan of both new and existing electric power plants to meet future electricity demand. We consider a stochastic optimization approach for this capacity expansion problem under demand and fuel price uncertainty. In a two-stage stochastic optimization model for GEP, … Read more

    A Counterexample to “Threshold Boolean form for joint probabilistic constraints with random technology matrix”

  • James R. Luedtke
    • Categories Stochastic Programming Tags , ,

    Recently, in the paper “Threshold Boolean form for joint probabilistic constraints with random technology matrix” (Math. Program. 147:391–427, 2014), Kogan and Lejeune proposed a set of mixed-integer programming formulations for probabilistically constrained stochastic programs having random constraint matrix and finite support distribution. We show that the proposed formulations do not in general correctly model such … Read more

    Maximizing a class of submodular utility functions with constraints

  • Shabbir Ahmed
  • Jiajin Yu
    • Categories 0-1 Programming, Cutting Plane Approaches, Stochastic Programming Tags , , , ,

    Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: $P = \cset{(w,x)\in \reals \times \set{0,1}^N}{w \leq f(a’x + d), b’x \leq B}$ where $N$ is a positive integer, $f:\reals \mapsto \reals$ is a concave function, $a, b \in \reals^N$ are nonnegative vectors, $d$ is a real … Read more

    Clustering-Based Preconditioning for Stochastic Programs

  • Yankai Cao
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Linear Programming, Quadratic Programming, Stochastic Programming

    We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem as opposed to cluster scenarios based on problem data alone, as is done in existing (outside-thesolver) approaches. We derive spectral … Read more