nonlinear programming

On the achievement of the complementary approximate Karush-Kuhn-Tucker conditions and algorithmic applications

  • Renan W. Prado
  • Sandra A. Santos
  • Lucas E. A. Simões
    • Categories Constrained Nonlinear Optimization Tags , ,

    Focusing on smooth constrained optimization problems, and inspired by the complementary approximate Karush-Kuhn-Tucker (CAKKT) conditions, this work introduces the weighted complementary Approximate Karush-Kuhn-Tucker (WCAKKT) conditions. They are shown to be verified not only by safeguarded augmented Lagrangian methods, but also by inexact restoration methods, inverse and logarithmic barrier methods, and a penalized algorithm for constrained … Read more

    A Reduced Jacobian Scheme with Full Convergence for Multicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Constrained Nonlinear Optimization, Linear Programming, Multi-Criteria Optimization Tags , , , , ,

    In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe in [JOTA, 179 (2018) 917–943] for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant … Read more

    A decomposition method for lasso problems with zero-sum constraint

  • Andrea Cristofari
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set technique, to identify the zero variables in the optimal solution, with a 2-coordinate descent scheme. At every iteration, the algorithm chooses … Read more

    A novel sequential optimality condition for smooth constrained optimization and algorithmic consequences

  • Renan W. Prado
  • Sandra A. Santos
  • Lucas E. A. Simões
    • Categories Constrained Nonlinear Optimization Tags , ,

    In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush-Kuhn-Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for nonsmooth constrained optimization problems. It is shown that the augmented Lagrangian method can generate limit points satisfying DCAKKT, and it is proved that such a condition is not related to … Read more

    An MISOCP-Based Decomposition Approach for the Unit Commitment Problem with AC Power Flows

  • Deniz Tuncer
  • Burak Kocuk
    • Categories Applications - Science and Engineering, Global Optimization Tags , , , ,

    Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental problems in short-term electric power systems planning that are traditionally solved sequentially. The state-of-the-art mostly uses a direct current flow approximation of the power flow equations in the UC-level and the generator commitments obtained are sent as input to the OPF-level. However, such an … Read more

    Modeling Design and Control Problems Involving Neural Network Surrogates

  • Dominic Yang
  • Prasanna Balaprakash
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Nonsmooth Optimization Tags , , , ,

    We consider nonlinear optimization problems that involve surrogate models represented by neural net-works. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific … Read more

    Regularized Step Directions in Conjugate Gradient Minimization for Machine Learning

  • Cassidy K. Buhler
  • Hande Benson
  • David F. Shanno
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    Conjugate gradient minimization methods (CGM) and their accelerated variants are widely used in machine learning applications. We focus on the use of cubic regularization to improve the CGM direction independent of the steplength (learning rate) computation. Using Shanno’s reformulation of CGM as a memoryless BFGS method, we derive new formulas for the regularized step direction, … Read more

    Scalable Parallel Nonlinear Optimization with PyNumero and Parapint

  • Jose Rodriguez
  • Robert Parker
  • Carl D. Laird
  • Bethany Nicholson
  • John D. Siirola
  • Michael Lee Bynum
    • Categories Nonlinear Optimization, Parallel Algorithms Tags ,

    We describe PyNumero, an open-source, object-oriented programming framework in Python that supports rapid development of performant parallel algorithms for structured nonlinear programming problems (NLP’s) using the Message Passing Interface (MPI). PyNumero provides three fundamental building blocks for developing NLP algorithms: a fast interface for calculating first and second derivatives with the AMPL Solver Library (ASL), … Read more

    Adaptable Energy Management System for Smart Buildings

  • Miguel F. Anjos
  • Juan A. Gomez-Herrera
  • Kenneth McKinnon
  • Ilaria Salerno
    • Categories Applications - OR and Management Sciences, Civil and Environmental Engineering, Optimization of Simulated Systems Tags , , , ,

    This paper presents a novel adaptable energy management system for smart buildings. In this framework we model the energy consumption of a living unit, and its energy exchange with the surroundings. We explicitly consider the impact of the outside environment and design features such as building orientation, automatic shading, and double facade. We formulate this … Read more

    A primal-dual interior-point relaxation method with adaptively updating barrier for nonlinear programs

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
    • Categories Nonlinear Optimization Tags , , , ,

    Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs. In the proposed method, the barrier parameter is updated in every step as done in interior-point methods for linear programs, which is prominently different from the existing interior-point methods … Read more