Constrained Nonlinear Optimization

A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

  • Frank E. Curtis
  • Victor M. Zavala
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as … Read more

    Second-order optimality and beyond: characterization and evaluation complexity in convexly-constrained nonlinear optimization

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    High-order optimality conditions for convexly-constrained nonlinear optimization problems are analyzed. A corresponding (expensive) measure of criticality for arbitrary order is proposed and extended to define high-order $\epsilon$-approximate critical points. This new measure is then used within a conceptual trust-region algorithm to show that, if derivatives of the objective function up to order $q \geq 1$ … Read more

    Online First-Order Framework for Robust Convex Optimization

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
    • Categories Constrained Nonlinear Optimization, Robust Optimization Tags , , ,

    Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in ever more larger scale. However, the traditional approaches for solving RO formulations based on building and solving robust counterparts or … Read more

    A derivative-free trust-region augmented Lagrangian algorithm

  • Charles Audet
  • Sébastien Le Digabel
  • Mathilde Peyrega
    • Categories Constrained Nonlinear Optimization

    We present a new derivative-free trust-region (DFTR) algorithm to solve general nonlinear constrained problems with the use of an augmented Lagrangian method. No derivatives are used, neither for the objective function nor for the constraints. An augmented Lagrangian method, known as an effective tool to solve equality and inequality constrained optimization problems with derivatives, is … Read more

    Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods

  • Björn Geißler
  • Antonio Morsi
  • Lars Schewe
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Detailed modeling of gas transport problems leads to nonlinear and nonconvex mixed-integer optimization or feasibility models (MINLPs) because both the incorporation of discrete controls of the network as well as accurate physical and technical modeling is required in order to achieve practical solutions. Hence, ignoring certain parts of the physics model is not valid for … Read more

    A progressive barrier derivative-free trust-region algorithm for constrained optimization

  • Charles Audet
  • Andrew R. Conn
  • Sébastien Le Digabel
  • Mathilde Peyrega
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    We study derivative-free constrained optimization problems and propose a trust-region method that builds linear or quadratic models around the best feasible and and around the best infeasible solutions found so far. These models are optimized within a trust region, and the progressive barrier methodology handles the constraints by progressively pushing the infeasible solutions toward the … Read more

    On a conjecture in second-order optimality conditions

  • Roger Behling
  • Gabriel Haeser
  • Alberto Ramos
  • Daiana O. Santos
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this paper we deal with optimality conditions that can be verified by a nonlinear optimization algorithm, where only a single Lagrange multiplier is avaliable. In particular, we deal with a conjecture formulated in [R. Andreani, J.M. Martinez, M.L. Schuverdt, “On second-order optimality conditions for nonlinear programming”, Optimization, 56:529–542, 2007], which states that whenever a … Read more

    New error measures and methods for realizing protein graphs from distance data

  • Claudia D'Ambrosio
  • Carlile Lavor
  • Leo Liberti
  • Nelson Maculan
  • Ky Vu
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications, Semi-definite Programming Tags , ,

    The interval Distance Geometry Problem (iDGP) consists in finding a realization in R^K of a simple undirected graph G=(V,E) with nonnegative intervals assigned to the edges in such a way that, for each edge, the Euclidean distance between the realization of the adjacent vertices is within the edge interval bounds. Our aim is to determine … Read more

    Order-based error for managing ensembles of surrogates in derivative-free optimization

  • Charles Audet
  • Michael Kokkolaras
  • Sébastien Le Digabel
  • Bastien Talgorn
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    We investigate surrogate-assisted strategies for derivative-free optimization using the mesh adaptive direct search (MADS) blackbox optimization algorithm. In particular, we build an ensemble of surrogate models to be used within the search step of MADS, and examine different methods for selecting the best model for a given problem at hand. To do so, we introduce … Read more

    A note on the squared slack variables technique for nonlinear optimization

  • Ellen H. Fukuda
  • Masao Fukushima
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In constrained nonlinear optimization, the squared slack variables can be used to transform a problem with inequality constraints into a problem containing only equality constraints. This reformulation is usually not considered in the modern literature, mainly because of possible numerical instabilities. However, this argument only concerns the development of algorithms, and nothing stops us in … Read more