Constrained Nonlinear Optimization

solar: A solar thermal power plant simulator for blackbox optimization benchmarking

  • Sébastien Le Digabel
  • Charles Audet
  • Xavier Lebeuf
  • Miguel Diago
  • Aïmen E. Gheribi
  • Christophe Tribes
    • Categories Constrained Nonlinear Optimization, Energy, Optimization Software Benchmark Tags , , ,

    This work introduces solar, a collection of  ten optimization problem instances for benchmarking blackbox optimization solvers. The instances present different design aspects of a concentrated solar power plant simulated by blackbox numerical models. The type of variables (discrete or continuous), dimensionality, and number and types of constraints (including hidden constraints)  differ across instances. Some are deterministic, others are stochastic … Read more

    Exploiting cone approximations in an augmented Lagrangian method for conic optimization

  • Mituhiro Fukuda
  • Walter Gómez
  • Gabriel Haeser
  • Leonardo M. Mito
    • Categories Cone Programming, Constrained Nonlinear Optimization Tags , , ,

    We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global convergence property in the sense that it generates a strong sequential optimality condition. In particular, a KKT point … Read more

    On the global convergence of a general class of augmented Lagrangian methods

  • Ernesto G. Birgin
  • Gabriel Haeser
  • Nelson Maculan
  • Lennin Mallma Ramirez
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In [E. G. Birgin, R. Castillo and J. M. Martínez, Computational Optimization and Applications 31, pp. 31-55, 2005], a general class of safeguarded augmented Lagrangian methods is introduced which includes a large number of different methods from the literature. Besides a numerical comparison including 65 different methods, primal-dual global convergence to a KKT point is … Read more

    Exploiting Sign Symmetries in Minimizing Sums of Rational Functions

  • Jie Wang
  • Feng Guo
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications, Semi-definite Programming Tags , , , ,

    This paper is devoted to the problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of sum of squares (SOS) relaxations that is dual to the generalized moment problem approach due to Bugarin, Henrion, and Lasserre. The investigation of the dual SOS aspect offers two benefits: 1) … Read more

    Approaches to iterative algorithms for solving nonlinear equations with an application in tomographic absorption spectroscopy

  • Francisco J. Aragón Artacho
  • Weiwei Cai
  • Yair Censor
  • Aviv Gibali
  • Chongyuan Shui
  • David Torregrosa-Belén
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupling, we consider a situation where straightforward translation to a fixed point problem is not possible because the operators that represent the … Read more

    A Bilevel Hierarchy of Strengthened Complex Moment Relaxations for Complex Polynomial Optimization

  • Jie Wang
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Semi-definite Programming Tags , , ,

    This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the normality of the so-called shift operators. The relaxation problem in this new hierarchy is parameterized by the usual relaxation order as well as … Read more

    Model Construction for Convex-Constrained Derivative-Free Optimization

  • Lindon Roberts
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the ability to construct sufficiently accurate approximations via interpolation, but the standard notions of accuracy (designed for unconstrained problems) may not be achievable by only sampling … Read more

    A Unified Approach for Maximizing Continuous $\gamma$-weakly DR-submodular Functions

  • Mohammad Pedramfar
  • Christopher Quinn
  • Vaneet Aggarwal
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , ,

    This paper presents a unified approach for maximizing continuous \(\gamma\)-weakly DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the convex feasible region. We consider settings where the oracle provides access to either the … Read more