Month: November 2023

Computing an approximation of the nondominated set of multi-objective mixed-integer nonlinear optimization problems

  • Leo Warnow
  • Gabriele Eichfelder
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    In practical applications, one often has not only one, but several objectives that need to be optimized simultaneously. What is more, modeling such real world problems usually involves using both, continuous and integer variables. This then results in multi-objective mixed-integer optimization problems, which are in focus of this paper. We present an approximation concept, called … Read more

    Local Convergence Analysis of an Inexact Trust-Region Method for Nonsmooth Optimization

  • Robert Baraldi
  • Drew P. Kouri
    • Categories Infinite Dimensional Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1–40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. This algorithm has demonstrated … Read more

    Efficient Proximal Subproblem Solvers for a Nonsmooth Trust-Region Method

  • Robert Baraldi
  • Drew P. Kouri
    • Categories Infinite Dimensional Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures … Read more

    Risk-Aware Security-Constrained Unit Commitment: Taming the Curse of Real-Time Volatility and Consumer Exposure

  • Daniel Bienstock
  • Yury Dvorkin
  • Cheng Guo
  • Robert Mieth
  • Jiayi Wang
    • Categories Applications - OR and Management Sciences Tags , ,

    We propose an enhancement to wholesale electricity markets whereby the exposure of consumers to increasingly large and volatile consumer payments arising as a byproduct of volatile real-time net loads — i.e., loads minus renewable outputs — and prices, both compared to day-ahead cleared values. We incorporate a robust estimate of such excess payments into the … Read more

    From Optimization to Control: Quasi Policy Iteration

  • Mohamad Amin Sharifi Kolarijani
  • Peyman Mohajerin Esfahani
    • Categories Convex Optimization, Dynamic Programming Tags , , , ,

    Recent control algorithms for Markov decision processes (MDPs) have been designed using an implicit analogy with well-established optimization algorithms. In this paper, we make this analogy explicit across four problem classes with a unified solution characterization. This novel framework, in turn, allows for a systematic transformation of algorithms from one domain to the other. In … Read more

    Handling of long-term storage in multi-horizon stochastic programs

  • Michal Kaut
    • Categories Stochastic Programming Tags

    This paper shows how to implement long-term storage in the multi-horizon modelling paradigm, expanding the range of problems this approach is applicable to. The presented implementation is based on the HyOpt optimization model, but the ideas should be transferable also to other models implementing the multi-horizon approach. We illustrate the effects of several different formulations … Read more

    A two-stage stochastic programming approach incorporating spatially-explicit fire scenarios for optimal firebreak placement

  • Sebastián Dávila
  • Andres Weintraub
  • Franco Quezada
  • Jaime
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    Ensuring the effective placement of firebreaks across the landscape is a critical issue in wildfire prevention, as their success relies on their ability to block the spread of future fires. To address this challenge, it is essential to recognize the stochastic nature of fires, which are highly unpredictable from start to finish. The issue is … Read more

    Exact Matrix Completion via High-Rank Matrices in Sum-of-Squares Relaxations

  • Sunyoung Kim
  • Godai Azuma
  • Makoto Yamashita
    • Categories Convex Optimization, Global Optimization Theory, Semi-definite Programming Tags , , , ,

    We study exact matrix completion from partially available data with hidden connectivity patterns. Exact matrix completion was shown to be possible recently by Cosse and Demanet in 2021 with Lasserre’s relaxation using the trace of the variable matrix as the objective function with given data structured in a chain format. In this study, we introduce … Read more

    Learning Optimal and Fair Policies for Online Allocation of Scarce Societal Resources from Data Collected in Deployment

  • Bill Tang
  • Çağıl Koçyiğit
  • Eric Rice
  • Phebe Vayanos
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    We study the problem of allocating scarce societal resources of different types (e.g., permanent housing, deceased donor kidneys for transplantation, ventilators) to heterogeneous allocatees on a waitlist (e.g., people experiencing homelessness, individuals suffering from end-stage renal disease, Covid-19 patients) based on their observed covariates. We leverage administrative data collected in deployment to design an online … Read more