Month: April 2017

MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations … Read more

    Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones

  • M. Seetharama Gowda
  • D. Sossa
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    Given a closed convex cone C in a finite dimensional real Hilbert space H, a weakly homogeneous map f:C–>H is a sum of two continuous maps h and g, where h is positively homogeneous of (positive) degree gamma on C and g(x)/||x||^gamma–>0 as ||x||–>infinity in C. Given such a map f, a nonempty closed convex … Read more

    Sample Average Approximation with Adaptive Importance Sampling

  • Mingbin Feng
  • Alvaro Maggiar
  • Jeremy Staum
  • Andreas Wächter
    • Categories Stochastic Programming Tags , , , ,

    We study sample average approximations under adaptive importance sampling in which the sample densities may depend on previous random samples. Based on a generic uniform law of large numbers, we establish uniform convergence of the sample average approximation to the true function. We obtain convergence of the optimal value and optimal solutions of the sample … Read more

    Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables

  • Alper Atamturk
  • Hyemin Jeon
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming Tags , , , ,

    We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities … Read more

    Convergence properties of a second order augmented Lagrangian method for mathematical programs with complementarity constraints

  • Roberto Andreani
  • Paulo J. S. Silva
  • Leonardo D. Secchin
    • Categories Complementarity and Variational Inequalities Tags , ,

    Mathematical Programs with Complementarity Constraints (MPCCs) are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications (CQs) for standard nonlinear optimization. Despite this fact, classical methods behaves well when applied to MPCCs. Recently, Izmailov, Solodov and Uskov proved that first order augmented Lagrangian methods, under a natural adaption of the … Read more

    Robust Multi-Period Vehicle Routing under Customer Order Uncertainty

  • Chrysanthos E. Gounaris
  • Anirudh Subramanyam
  • Jose M. Lainez-Aguirre
  • Frank Mufalli
  • Jose M. Pinto
    • Categories Robust Optimization, Transportation Tags , ,

    In this paper, we study multi-period vehicle routing problems where the aim is to determine a minimum cost visit schedule and associated routing plan for each period using capacity-constrained vehicles. In our setting, we allow for customer service requests that are received dynamically over the planning horizon. In order to guarantee the generation of routing … Read more

    Decomposition Algorithms for Distributionally Robust Optimization using Wasserstein Metric

  • Fengqiao Luo
  • Sanjay Mehrotra
    • Categories Data-Mining, Robust Optimization, Semi-infinite Programming Tags , , , ,

    We study distributionally robust optimization (DRO) problems where the ambiguity set is de ned using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-in nite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, … Read more

    FiberSCIP – A shared memory parallelization of SCIP

  • Stefan Heinz
  • Yuji Shinano
  • Stefan Vigerske
  • Michael Winkler
    • Categories Integer Programming, Parallel Algorithms

    Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There … Read more

    Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Running Time

  • Mengdi Wang
    • Categories Dynamic Programming, Linear Programming Tags , , , , , ,

    We propose a randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality, the algorithm adaptively samples state transitions and makes exponentiated primal-dual updates. We show that it finds an ε-optimal policy using nearly-linear running time in the worst case. For Markov decision processes that … Read more

    Optimal Installation for Electric Vehicle Wireless Charging Lanes

  • Mashrur Chowdhury
  • MD Zadid Khan
  • Ilya Safro
  • Hayato Ushijima-Mwesigwa
    • Categories 0-1 Programming, Civil and Environmental Engineering, Transportation

    Range anxiety, the persistent worry about not having enough battery power to complete a trip, remains one of the major obstacles to widespread electric-vehicle adoption. As cities look to attract more users to adopt electric vehicles, the emergence of wireless in-motion car charging technology presents itself as a solution to range anxiety. For a limited … Read more