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

    The Role of Level-Set Geometry on the Performance of PDHG for Conic Linear Optimization

  • Zikai Xiong
  • Robert M. Freund
    • Categories Convex Optimization, Linear Programming, Linear, Cone and Semidefinite Programming Tags , , , , ,

    We consider solving huge-scale instances of (convex) conic linear optimization problems, at the scale where matrix-factorization-free methods are attractive or necessary. The restarted primal-dual hybrid gradient method (rPDHG) — with heuristic enhancements and GPU implementation — has been very successful in solving huge-scale linear programming (LP) problems; however its application to more general conic convex … Read more

    Nonconvex optimization problems involving the Euclidean norm: Challenges, progress, and opportunities

  • Anatoliy Kuznetsov
  • Nikolaos Sahinidis
    • Categories Global Optimization, Optimization Software Benchmark Tags , , ,

    The field of global optimization has advanced significantly over the past three decades. Yet, the solution of even small instances of many nonconvex optimization problems involving the Euclidean norm to global optimality remains beyond the reach of modern global optimization methods. These problems include numerous well-known and high-impact open research questions from a diverse collection … Read more

    Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization

  • Immanuel M. Bomze
  • Bo Peng
  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Semi-definite Programming Tags , , , ,

    The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the simplest polytope/compact feasible set). As a problem class, StQPs may be nonconvex with an exponential number of inefficient local solutions. StQPs arise in a … Read more

    Efficient Project Scheduling with Autonomous Learning Opportunities

  • Alessandro Hill
  • Thomas Vossen
    • Categories Combinatorial Optimization, Scheduling

    We consider novel project scheduling problems in which the experience gained from completing selected activities can be used to accelerate subsequent activities. Given a set of potential learning opportunities, our model aims to identify the opportunities that result in a maximum reduction of the project makespan when scheduled in sequence. Accounting for the impact of … 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

    A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

  • Man-Chung Yue
  • Yves Rychener
  • Daniel Kuhn
  • Viet Anh Nguyen
    • Categories Robust Optimization, Stochastic Programming

    The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically – without compelling theoretical justification – or optimally in view of restrictive distributional assumptions. In this paper, we propose a principled approach to construct covariance … Read more

    On the integrality gap of the Complete Metric Steiner Tree Problem via a novel formulation

  • Ambrogio Maria Bernardelli
  • Eleonora Vercesi
  • Stefano Gualandi
  • Monaldo Mastrolilli
  • Luca Maria Gambardella
    • Categories Combinatorial Optimization, Graphs and Matroids, Linear Programming Tags , ,

    In this work, we study the metric Steiner Tree problem on graphs focusing on computing lower bounds for the integrality gap of the bi-directed cut (BCR) formulation and introducing a novel formulation, the Complete Metric (CM) model, specifically designed to address the weakness of the BCR formulation on metric instances. A key contribution of our … Read more

    On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization

  • Andrea Cristofari
  • Marianna De Santis
  • Stefano Lucidi
    • Categories Multi-Criteria Optimization Tags , ,

    Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of … Read more