Month: September 2024

Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees

  • Zhaosong Lu
  • Sanyou Mei
  • Yifeng Xiao
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an \(\epsilon\)-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy \(\epsilon\). However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, … Read more

    An inertial projective splitting method for the sum of two maximal monotone operators

  • Majela Pentón Machado
    • Categories Convex and Nonsmooth Optimization, Global Optimization, Other Topics Tags

    We propose a projective splitting type method to solve the problem of finding a zero of the sum of two maximal monotone operators. Our method considers inertial and relaxation steps, and also allows inexact solutions of the proximal subproblems within a relative-error criterion.We study the asymptotic convergence of the method, as well as its iteration-complexity. … Read more

    Estimating the Unobservable Components of Electricity Demand Response with Inverse Optimization

  • Adrian Esteban Perez
    • Categories Energy, Statistics, Stochastic Programming Tags , , , , ,

    Understanding and predicting the electricity demand responses to prices are critical activities for system operators, retailers, and regulators. While conventional machine learning and time series analyses have been adequate for the routine demand patterns that have adapted only slowly over many years, the emergence of active consumers with flexible assets such as solar-plus-storage systems, and … Read more

    Robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty

  • Alejandro Crema
    • Categories Approximation Algorithms, Combinatorial Optimization, Robust Optimization Tags , , , ,

    We present an algorithm for finding near-optimal solutions to robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty. We incorporate a heuristic for generating feasible solutions in a standard row generation approach. Experimental results are presented for set covering, simple plant location, and min-knapsack problems under a discrete-budgeted interdiction uncertainty set introduced in this … Read more

    Randomized Roundings for a Mixed-Integer Elliptic Control System

  • Martin T. Köhler
  • Lauri Kröger
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , ,

    We present randomized reconstruction approaches for optimal solutions to mixed-integer elliptic PDE control systems. Approximation properties and relations to sum-up rounding are derived using the cut norm. This enables us to dispose of space-filling curves required for sum-up rounding. Rates of almost sure convergence in the cut norm and the SUR norm in control space … Read more

    Exact SDP relaxations for a class of quadratic programs with finite and infinite quadratic constraints

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Cone Programming, Semi-definite Programming Tags , , ,

    We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality constraints (semi-infinite QCQPs). Specifically, we present two sufficient conditions on the feasible region under which the QCQP, with any quadratic objective function over the … Read more

    Global convergence of a second-order augmented Lagrangian method under an error bound condition

  • Renan W. Prado
  • Leonardo D. Secchin
  • Gabriel Haeser
  • Roberto Andreani
  • María Laura Schuverdt
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    This work deals with convergence to points satisfying the weak second-order necessary optimality conditions of a second-order safeguarded augmented Lagrangian method from the literature. To this end, we propose a new second-order sequential optimality condition that is, in a certain way, based on the iterates generated by the algorithm itself. This also allows us to … Read more

    A homotopy for the reliable estimation of model parameters in chromatography processes

  • Dominik H. Cebulla
  • Christian Kirches
  • Andreas Potschka
    • Categories Chemical Engineering, Nonlinear Systems and Least-Squares, Optimization of Systems modeled by PDEs Tags , , ,

    Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more

    Global convergence of an augmented Lagrangian method for nonlinear programming via Riemannian optimization

  • Roberto Andreani
  • Kelvin Rodrigues Couto
  • Orizon Pereira Ferreira
  • Gabriel Haeser
  • Leandro Fonseca Prudente
    • Categories Nonlinear Optimization Tags , , ,

    Considering a standard nonlinear programming problem, one may view a subset of the equality constraints as an embedded Riemannian manifold. In this paper we investigate the differences between the Euclidean and the Riemannian approach for this problem. It is well known that the linear independence constraint qualification for both approaches are equivalent. However, when considering … Read more

    Combinatorial Robust Optimization with Decision-Dependent Information Discovery and Polyhedral Uncertainty

  • Jérémy Omer
  • Michael Poss
    • Categories Combinatorial Optimization, Robust Optimization Tags , , ,

    Given a nominal combinatorial optimization problem, we consider a robust two-stages variant with polyhedral cost uncertainty, called Decision-Dependent Information Discovery (DDID). In the first stage, DDID selects a subset of uncertain cost coefficients to be observed, and in the second-stage, DDID selects a solution to the nominal problem, where the remaining cost coefficients are still … Read more