Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming

  • Alexander Shapiro
    • Categories Robust Optimization, Stochastic Programming Tags , , , , , ,

    In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more

    Stochastic dual dynamic programming with stagewise dependent objective uncertainty

  • Regan Baucke
  • Anthony Downward
  • Oscar Dowson
    • Categories Stochastic Programming Tags , , , ,

    We present a new algorithm for solving linear multistage stochastic programming problems with objective function coefficients modeled as a stochastic process. This algorithm overcomes the difficulties of existing methods which require discretization. Using an argument based on the finiteness of the set of possible cuts, we prove that the algorithm converges almost surely. Finally, we … Read more

    Regional Complexity Analysis of Algorithms for Nonconvex Smooth Optimization

  • Frank E. Curtis
  • Daniel P. Robinson
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an objective function, an upper bound on the number of iterations (or function or derivative evaluations) required until a pth-order stationarity condition is approximately satisfied. This arguably … Read more

    The condition of a function relative to a polytope

  • David H. Gutman
  • Javier F. Peña
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , ,

    The condition number of a smooth convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In particular, the condition number of a quadratic convex function is precisely the square of the diameter-to-width ratio of a canonical ellipsoid associated to the function. Furthermore, the … Read more

    A structured quasi-Newton algorithm for optimizing with incomplete Hessian information

  • Mihai Anitescu
  • Naiyuan Chiang
  • Cosmin G. Petra
    • Categories Unconstrained Optimization Tags , , ,

    We present a structured quasi-Newton algorithm for unconstrained optimization problems that have unavailable second-order derivatives or Hessian terms. We provide a formal derivation of the well-known BFGS secant update formula that approximates only the missing Hessian terms, and we propose a line-search quasi-Newton algorithm based on a modification of Wolfe conditions that converges to first-order … Read more

    Optimal Black Start Allocation for Power System Restoration

  • Shmuel Oren
  • Deepak Rajan
  • Georgios Patsakis
  • Jennifer Rios
    • Categories (Mixed) Integer Linear Programming, Energy Tags , ,

    Equipment failures, operator errors, natural disasters and cyber-attacks can and have caused extended blackouts of the electric grid. Even though such events are rare, preparedness for them is critical because extended power outages endanger human lives, compromise national security, or result in economic losses of billions of dollars. Since most of the generating units cannot … Read more

    Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks

  • Martin Robinius
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Detlef Stolten
  • Lara Welder
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to … Read more

    A Decision Tool based on a Multi-Objective Methodology for designing High-Pressure Thermal Treatments in Food Industry

  • Miriam R. Ferrández
  • Benjamin Ivorra
  • Pilar M. Ortigosa
  • Ángel M. Ramos
  • Juana L. Redondo
    • Categories Meta Heuristics, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    In this work, we propose a methodology for designing High-Pressure Thermal processes for food treatment. This approach is based on a multi-objective preference-based evolutionary optimization algorithm, called WASF-GA, combined with a decision strategy which provides the food engineer with the best treatment in accordance with some quality requirements. The resulting method is compared to a … Read more

    Strong formulations for quadratic optimization with M-matrices and semi-continuous variables

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

    We study quadratic optimization with semi-continuous variables and an M-matrix, i.e., PSD with non-positive off-diagonal entries. This structure arises in image segmentation, portfolio optimization, as well as a substructure of general quadratic optimization problems. We prove, under mild assumptions, that the minimization problem is solvable in polynomial time by showing its equivalence to a submodular … Read more

    A Shifted Primal-Dual Interior Method for Nonlinear Optimization

  • Philip E. Gill
  • Vyacheslav Kungurtsev
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    Interior methods provide an effective approach for the treatment of inequality constraints in nonlinearly constrained optimization. A new primal-dual interior method is proposed based on minimizing a sequence of shifted primal-dual penalty-barrier functions. Certain global convergence properties are established. In particular, it is shown that every limit point is either an infeasible stationary point, or … Read more