Month: June 2021

Alternative Regularizations for OA Algorithms for Convex MINLP

  • David E. Bernal Neira
  • Ignacio E. Grossmann
  • Jan Kronqvist
  • Zedong Peng
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Nonsmooth Optimization

    In this work, we extend the regularization framework from Kronqvist et al. (https://doi.org/10.1007/s10107-018-1356-3) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance-metrics and Lagrangean approximations, used in the projection problem for finding new … Read more

    Analysis of the Frank-Wolfe Method for Convex Composite Optimization involving a Logarithmically-Homogeneous Barrier

  • Robert M. Freund
  • Renbo Zhao
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , , , , ,

    We present and analyze a new generalized Frank-Wolfe method for the composite optimization problem (P): F*:= min_x f(Ax) + h(x), where f is a \theta-logarithmically-homogeneous self-concordant barrier and the function h has bounded domain but is possibly non-smooth. We show that our generalized Frank-Wolfe method requires O((Gap_0 + \theta + Var_h)\ln(\delta_0) + (\theta + Var_h)^2/\epsilon) … Read more

    A Gentle and Incomplete Introduction to Bilevel Optimization

  • Yasmine Beck
  • Martin Schmidt
    • Categories Other Topics Tags ,

    These are lecture notes on bilevel optimization. The class of bilevel optimization problems is formally introduced and motivated using examples from different fields. Afterward, the main focus is on how to solve linear and mixed-integer linear bilevel optimization problems. To this end, we first consider various single-level reformulations of bilevel optimization problems with linear or … Read more

    Barrier Methods Based on Jordan-Hilbert Algebras for Stochastic Optimization in Spin Factors

  • Baha Alzalg
    • Categories Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    We present decomposition logarithmic-barrier interior-point methods based on unital Jordan-Hilbert algebras for infinite-dimensional stochastic second-order cone programming problems in spin factors. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best … Read more

    A Homogeneous Predictor-Corrector Algorithm for Stochastic Nonsymmetric Convex Conic Optimization With Discrete Support

  • Baha Alzalg
  • Mohammad Alabedalhadi
    • Categories Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , ,

    We consider a stochastic convex optimization problem over nonsymmetric cones with discrete support. This class of optimization problems has not been studied yet. By using a logarithmically homogeneous self-concordant barrier function, we present a homogeneous predictor-corrector interior-point algorithm for solving stochastic nonsymmetric conic optimization problems. We also derive an iteration bound for the proposed algorithm. … Read more

    An Algorithm-Independent Measure of Progress for Linear Constraint Propagation

  • Ambros Gleixner
  • Sebastian Pokutta
  • Boro Sofranac
    • Categories (Mixed) Integer Linear Programming Tags ,

    Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a … Read more

    Long-Run Optimal Pricing in Electricity Markets with Non-Convex Costs

  • Conleigh Byers
  • Gabriela Hug
    • Categories Applications - OR and Management Sciences, Integer Programming Tags , ,

    Determining optimal prices in non-convex markets remains an unsolved challenge. Non-convex costs are critical in electricity markets, as startup costs and minimum operating levels yield a non-convex optimal value function over demand levels. While past research largely focuses on the performance of different non-convex pricing frameworks in the short-run, we determine long-run adapted resource mixes … Read more

    RSOME in Python: An Open-Source Package for Robust Stochastic Optimization Made Easy

  • Peng Xiong
  • Zhi Chen
    • Categories Modeling Languages and Systems, Robust Optimization Tags , , ,

    We develop a Python package called RSOME for modeling a wide spectrum of robust and distributionally robust optimization problems. RSOME serves as a modeling platform for formulating various optimization problems subject to distributional ambiguity in a highly readable and mathematically intuitive manner. Compared with the MATLAB version, RSOME in Python is more versatile and well … Read more

    Optimal Eco-Routing for Hybrid Vehicles with Mechanistic/Data-Driven Powertrain Model Embedded

  • Adrian Caspari
  • Alexander Mitsos
  • Steffen Fahr
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Transportation Tags , , , , , ,

    Hybrid Electric Vehicles (HEVs) are regarded as an important (transition) element of sustainable transportation. Exploiting the full potential of HEVs requires (i) a suitable route selection and (ii) suitable power management, i.e., deciding on the split between combustion engine and electric motor usage as well as the mode of the electric motor, i.e., driving or … Read more

    Distributionally Robust Optimization with Markovian Data

  • Daniel Kuhn
  • Tobias Sutter
  • Mengmeng Li
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with d states. We propose a data-driven distributionally robust optimization model to estimate the problem’s objective function and optimal solution. By leveraging results from … Read more