Month: July 2023

Modified Monotone Policy Iteration for Interpretable Policies in Markov Decision Processes and the Impact of State Ordering Rules

  • Sun Ju Lee
  • Xingyu Gong
  • Gian-Gabriel Garcia
    • Categories Dynamic Programming

    Optimizing interpretable policies for Markov Decision Processes (MDPs) can be computationally intractable for large-scale MDPs, e.g., for monotone policies, the optimal interpretable policy depends on the initial state distribution, precluding standard dynamic programming techniques. Previous work has proposed Monotone Policy Iteration (MPI) to produce a feasible solution for warm starting a Mixed Integer Linear Program … Read more

    A more efficient reformulation of complex SDP as real SDP

  • Jie Wang
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , , ,

    This note proposes a new reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting inner structure of the complex SDP relaxations. Various numerical examples demonstrate that our new … Read more

    Exact convergence rate of the last iterate in subgradient methods

  • Moslem Zamani
  • François Glineur
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , ,

    We study the convergence of the last iterate in subgradient methods applied to the minimization of a nonsmooth convex function with bounded subgradients. We first introduce a proof technique that generalizes the standard analysis of subgradient methods. It is based on tracking the distance between the current iterate and a different reference point at each … Read more

    Essays on Average Incremental Cost Pricing for Independent System Operators

  • Richard O'Neill
  • Yonghong Chen
  • Brent Eldridge
    • Categories (Mixed) Integer Linear Programming Tags ,

    In a series of essays, we introduce average incremental cost (AIC) pricing and present examples to help understand its advantages. In non-convex markets, AIC pricing is the rough equivalent to marginal cost pricing in convex markets. We present a qualitative comparison of current ISO pricing methods and the AIC approach. We argue that AIC better … Read more

    One-Pass Average Incremental Cost Pricing

  • Richard O'Neill
  • Yonghong Chen
    • Categories (Mixed) Integer Linear Programming Tags ,

    Since the inception of ISOs, Locational Marginal Prices (LMPs) alone were not incentive compatible because an auction winner who offered its avoidable costs could lose money at the LMP. ISOs used make-whole payments to ensure market participants did not lose money. Make-whole payments were not public creating transparency issues. Over time, the ISOs employed methods … Read more

    Inexact Direct-Search Methods for Bilevel Optimization Problems

  • Youssef Diouane
  • Vyacheslav Kungurtsev
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Optimization in Data Science

    In this work, we introduce new direct search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy black box oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct search schemes in … Read more

    Planning a Zero-Emission Mixed-Fleet Public Bus System with Minimal Life Cycle Cost

  • Nathalie Frieß
  • Ulrich Pferschy
    • Categories Applications - OR and Management Sciences, Transportation Tags , , , , ,

    The variety of available technology options for the operation of zero-emission bus systems gives rise to the problem of finding an optimal technology decision for bus operators. Among others, overnight charging, opportunity charging and hydrogen-based technology options are frequently pursued technological solutions. As their operating conditions are strongly influenced by the urban context, an optimal … Read more

    A Short Proof of Tight Bounds on the Smallest Support Size of Integer Solutions to Linear Equations

  • Yatharth Dubey
  • Siyue Liu
    • Categories Integer Programming, Other Topics Tags ,

    In this note, we study the size of the support of solutions to linear Diophantine equations $Ax=b, ~x\in\Z^n$ where $A\in\Z^{m\times n}, b\in\Z^n$. We give an asymptotically tight upper bound on the smallest support size, parameterized by $\|A\|_\infty$ and $m$, and taken as a worst case over all $b$ such that the above system has a … Read more

    Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems

  • Leandro Fonseca Prudente
  • D. R. Souza
    • Categories Multi-Criteria Optimization Tags , , , , , ,

    We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration … Read more

    On the Computation of Restricted Normal Cones

  • Mario Jelitte
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    Restricted normal cones are of interest, for instance, in the theory of local error bounds, where they have recently been used to characterize the exis- tence of a constrained Lipschitzian error bound. In this paper, we establish rela- tions between two concepts for restricted normals. The first of these concepts was introduced in the late … Read more