Stochastic Programming

Convergence of stochastic average approximation for stochastic optimization problems with mixed expectation and per-scenario constraints

  • Mihai Anitescu
  • Birge John
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , ,

    We present a framework for ensuring convergence of sample average approximations to stochastic optimization problems that include expectation constraints in addition to per-scenario constraints. Citation Preprint ANL/MCS 1562-1108 Article Download View Convergence of stochastic average approximation for stochastic optimization problems with mixed expectation and per-scenario constraints

    Optimal Scenario Tree Reduction for Stochastic Streamflows in Power Generation Planning Problems

  • J.M. Damazio
  • Welington de Oliveira
  • Maria Elvira P. Maceira
  • Claudia Sagastizábal
  • D.D. Penna
    • Categories Stochastic Programming Tags , ,

    The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences … Read more

    Optimization of Real Asset Portfolio using a Coherent Risk Measure: Application to Oil and Energy Industries

  • Sergio V.B. Bruno
  • Claudia Sagastizábal
    • Categories Applications - OR and Management Sciences, Finance and Economics, Stochastic Programming

    In many industries, investment is part of the most important planning decisions. In past decades, mathematical programming models have been widely used in capacity planning and facility location to support investment decisions. Such initial techniques evolved to the use of enterprise portfolio management, very common in the energy industry. Increasing concern on risk made of … Read more

    Consideration of Gas Supply Contracts with Take-or-pay Clauses in the Brazilian Long-term Energy Planning

  • Maria Elvira P. Maceira
  • Claudia Sagastizábal
  • Leonardo A. M. Moraes
    • Categories Applications - Science and Engineering, Stochastic Programming Tags , , ,

    In Brazil’s long-term energy planning, the dispatch of thermal plants usually varies along a year. Such variation is essentially due to the predominance of the hydraulic mix in the system electric energy supply. For this reason, without preventive measures, a highly irregular cash flow occurs for natural gas (NG) providers, who supply gas for electric … Read more

    Incremental-like Bundle Methods with Application to Energy Planning

  • Grégory Emiel
  • Claudia Sagastizábal
    • Categories Nonsmooth Optimization, Production and Logistics, Stochastic Programming Tags , , ,

    An important field of application of non-smooth optimization refers to decomposition of large-scale or complex problems by Lagrangian duality. In this setting, the dual problem consists in maximizing a concave non-smooth function that is defined as the sum of sub-functions. The evaluation of each sub-function requires solving a specific optimization sub-problem, with specific computational complexity. … Read more

    A Cutting Surface Method for Uncertain Linear Programs with Polyhedral Stochastic Dominance Constraints

  • Tito Homem-de-Mello
  • Sanjay Mehrotra
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , ,

    In this paper we study linear optimization problems with multi-dimensional linear positive second-order stochastic dominance constraints. By using the polyhedral properties of the second- order linear dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral … Read more

    A Multistage Stochastic Programming Approach to Open Pit Mine Production Scheduling with Uncertain Geology

  • Natashia Boland
  • Gary Froyland
  • Irina Dumitrescu
    • Categories Applications - OR and Management Sciences, Integer Programming, Stochastic Programming Tags , , ,

    The Open Pit Mine Production Scheduling Problem (OPMPSP) studied in recent years is usually based on a single geological estimate of material to be excavated and processed over a number of decades. However techniques have now been developed to generate multiple stochastic geological estimates that more accurately describe the uncertain geology. While some attempts have … Read more

    A Framework for Optimization under Ambiguity

  • David Wozabal
    • Categories Global Optimization Applications, Robust Optimization, Stochastic Programming

    In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P enables the construction of non-parametric ambiguity sets as Kantorovich balls around P. The resulting robustified problems are infinite optimization problems and can therefore not be solved … Read more

    Chance-constrained optimization via randomization: feasibility and optimality

  • Marco C. Campi
  • Simone Garatti
    • Categories Convex Optimization, Semi-infinite Programming, Stochastic Programming Tags , ,

    In this paper we study the link between a semi-infinite chance-constrained optimization problem and its randomized version, i.e. the problem obtained by sampling a finite number of its constraints. Extending previous results on the feasibility of randomized convex programs, we establish here the feasibility of the solution obtained after the elimination of a portion of … Read more

    Progressive Hedging Innovations for a Class of Stochastic Resource Allocation Problems

  • David Strip
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories Production and Logistics, Stochastic Programming Tags , ,

    Progressive hedging (PH) is a scenario-based decomposition technique for solving stochastic programs. While PH has been successfully applied to a number of problems, a variety of issues arise when implementing PH in practice, especially when dealing with very difficult or large-scale mixed-integer problems. In particular, decisions must be made regarding the value of the penalty … Read more