Global Optimization Applications

A graphical framework for global optimization of mixed-integer nonlinear programs

  • Danial Davarnia
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Applications, Global Optimization Theory Tags , , , , ,

    While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of maturity. Various problem structures across different application domains remain challenging to model and solve using modern global solvers, primarily due to the lack … Read more

    Globally Convergent Derivative-Free Methods in Nonconvex Optimization with and without Noise

  • Dat Tran
    • Categories Approximation Algorithms, Global Optimization Applications, Unconstrained Optimization

    This paper addresses the study of nonconvex derivative-free optimization problems, where only information of either smooth objective functions or their noisy approximations is available. General derivative-free methods are proposed for minimizing differentiable (not necessarily convex) functions with globally Lipschitz continuous gradients, where the accuracy of approximate gradients is interacting with stepsizes and exact gradient values. … Read more

    BattOpt: Optimal Facility Planning for Electric Vehicle Battery Recycling

  • Matthew Brun
  • Xu Andy Sun
    • Categories Energy, Global Optimization Applications, Stochastic Programming Tags , , ,

    The electric vehicle (EV) battery supply chain will face challenges in sourcing scarce, expensive minerals required for manufacturing and in disposing of hazardous retired batteries. Integrating recycling technology into the supply chain has the potential to alleviate these issues; however, players in the battery market must design investment plans for recycling facilities. In this paper, … 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

    Revisiting the fitting of the Nelson-Siegel and Svensson models

  • Dirk Banholzer
  • Jörg Fliege
  • Ralf Werner
    • Categories Finance and Economics, Global Optimization Applications, Nonlinear Systems and Least-Squares Tags , , , , ,

    The Nelson-Siegel and the Svensson models are two of the most widely used models for the term structure of interest rates. Even though the models are quite simple and intuitive, fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, a novel mathematical analysis of the fitting problem … Read more

    Exploring Nonlinear Distance Metrics for Lipschitz Constant Estimation in Lower Bound Construction for Global Optimization

  • Mohammadsina Almasi
  • Hadis Anahideh
  • Jay Rosenberger
    • Categories Bound-constrained Optimization, Global Optimization, Global Optimization Applications Tags , , , ,

    Bounds play a crucial role in guiding optimization algorithms, improving their speed and quality, and providing optimality gaps. While Lipschitz constant-based lower bound construction is an effective technique, the quality of the linear bounds depends on the function’s topological properties. In this research, we improve upon this by incorporating nonlinear distance metrics and surrogate approximations … Read more

    Refined TSSOS

  • Daria Shaydurova
  • Volker Kaibel
  • Sebastian Sager
    • Categories Global Optimization Applications, Nonlinear Optimization, Semi-definite Programming Tags , , , ,

    The moment-sum of squares hierarchy by Lasserre has become an established technique for solving polynomial optimization problems. It provides a monotonically increasing series of tight bounds, but has well-known scalability limitations. For structured optimization problems, the term-sparsity SOS (TSSOS) approach scales much better due to block-diagonal matrices, obtained by completing the connected components of adjacency … Read more

    Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert

  • Ryan Cory-Wright
  • Cristina Cornelio
  • Sanjeeb Dash
  • Bachir El Khadir
  • Lior Horesh
    • Categories Basic Sciences Applications, Global Optimization Applications, Semi-definite Programming Tags , , ,

    The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in … Read more

    Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme

  • Lakhdar Chiter
    • Categories Global Optimization Applications, Other Topics Tags

    In this paper we consider a global optimization problem, where the objective function is supposed to be Lipschitz-continuous with an unknown Lipschitz constant. Based on the recently introduced BIRECT (BIsection of RECTangles) algorithm, a new diagonal partitioning and sampling scheme is introduced. 0ur framework, called BIRECT-V (where V stands for vertices), combines bisection with sampling … Read more

    A Moment-SOS Hierarchy for Robust Polynomial Matrix Inequality Optimization with SOS-Convexity

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

    We study a class of polynomial optimization problems with a robust polynomial matrix inequality constraint for which the uncertainty set is defined also by a polynomial matrix inequality (including robust polynomial semidefinite programs as a special case). Under certain SOS-convexity assumptions, we construct a hierarchy of moment-SOS relaxations for this problem to obtain convergent upper … Read more