Optimal participation of energy communities in electricity markets under uncertainty. A multi-stage stochastic programming approach

  • Albert Solà Vilalta
  • Ignasi Mañé Bosch
  • F.-Javier Heredia
    • Categories Energy, Stochastic Programming Tags , , ,

    We propose a multi-stage stochastic programming model for the optimal participation of energy communities in electricity markets. The multi-stage aspect captures the different times at which variable renewable generation and electricity prices are observed. This results in large-scale optimization problem instances containing large scenario trees with 34 stages, to which scenario reduction techniques are applied. … Read more

    On vehicle routing problems with stochastic demands — Generic integer L-shaped formulations

  • Matheus Jun Ota
  • Ricardo Fukasawa
    • Categories Branch and Cut Algorithms, Stochastic Programming, Transportation Tags , , ,

    We study a broad class of vehicle routing problems in which the cost of a route is allowed to be any nonnegative rational value computable in polynomial time in the input size. To address this class, we introduce a unifying framework that generalizes existing integer L-shaped (ILS) formulations developed for vehicle routing problems with stochastic … Read more

    Continuous-time Analysis of a Stochastic ADMM Method for Nonconvex Composite Optimization

  • Jiahong Guo
  • Xiao Wang
  • Xiantao Xiao
    • Categories Nonlinear Optimization, Unconstrained Optimization

    In this paper, we focus on nonconvex composite optimization, whose objective is the sum of a smooth but possibly nonconvex function and a composition of a weakly convex function coupled with a linear operator. By leveraging a smoothing technique based on Moreau envelope, we propose a stochastic proximal linearized ADMM algorithm (SPLA). To understand its … Read more

    On Integer Programming for the Binarized Neural Network Verification Problem

  • Woojin Kim
  • James R. Luedtke
    • Categories Integer Programming Tags , ,

    Binarized neural networks (BNNs) are feedforward neural networks with binary weights and activation functions. In the context of using a BNN for classification, the verification problem seeks to determine whether a small perturbation of a given input can lead it to be misclassified by the BNN, and the robustness of the BNN can be measured … Read more

    Progressively Sampled Equality-Constrained Optimization

  • Frank E. Curtis
  • Lingjun Guo
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the constraints are defined by an expectation or an average over a large (finite) number of terms. The main idea of the algorithm is to solve a sequence of equality-constrained problems, each involving a finite sample of constraint-function terms, over which … Read more

    A Riemannian AdaGrad-Norm Method

  • Glaydston Bento
  • Geovani Nunes Grapiglia
  • Mauricio Louzeiro
  • Daoping Zhang
    • Categories Generalized Convexity/Monoticity, Global Optimization Applications, Nonlinear Optimization Tags , , , ,

    We propose a manifold AdaGrad-Norm method (\textsc{MAdaGrad}), which extends the norm version of AdaGrad (AdaGrad-Norm) to Riemannian optimization. In contrast to line-search schemes, which may require several exponential map computations per iteration, \textsc{MAdaGrad} requires only one. Assuming the objective function $f$ has Lipschitz continuous Riemannian gradient, we show that the method requires at most $\mathcal{O}(\varepsilon^{-2})$ … Read more

    On the Convergence and Properties of a Proximal-Gradient Method on Hadamard Manifolds

  • Glaydston Bento
  • Claudemir Rodrigues Santiago
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Nonsmooth Optimization Tags , , ,

    In this paper, we address composite optimization problems on Hadamard manifolds, where the objective function is given by the sum of a smooth term (not necessarily convex) and a convex term (not necessarily differentiable). To solve this problem, we develop a proximal gradient method defined directly on the manifold, employing a strategy that enforces monotonicity … Read more

    Machine Learning Algorithms for Improving Black Box Optimization Solvers

  • Morteza Kimiaei
  • Vyacheslav Kungurtsev
    • Categories Global Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , , ,

    Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods—line search, direct search, and model-based solvers such as Bayesian optimization—form the backbone of BBO, yet often struggle in high-dimensional, noisy, or mixed-integer settings. Recent advances use machine learning (ML) and reinforcement learning (RL) to … Read more

    Sequential test sampling for stochastic derivative-free optimization

  • Anjie Ding
  • Francesco Rinaldi
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , ,

    In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial step, i.e., the true reduction in the objective function value that would be achieved by moving from the current point to the … Read more

    New insights and algorithms for optimal diagonal preconditioning

  • Saeed Ghadimi
  • Woosuk L. Jung
  • Arnesh Sujanani
  • David Torregrosa-Belén
  • Henry Wolkowicz
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization, Optimization in Data Science Tags , , , ,

    Preconditioning (scaling) is essential in many areas of mathematics, and in particular in optimization. In this work, we study the problem of finding an optimal diagonal preconditioner. We focus on minimizing two different notions of condition number: the classical, worst-case type, \(\kappa\)-condition number, and the more averaging motivated \(\omega\)-condition number. We provide affine based pseudoconvex … Read more