Month: June 2024

Floorplanning with I/O assignment via feasibility-seeking and superiorization methods

  • ShanYu
  • Yair Censor
  • Guojie Luo
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, VLSI layout Tags , , , , , ,

    The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be expressed as the union of convex sets. However, conventional projection-based algorithms for feasibility-seeking do not guarantee … Read more

    An exponential cone representation of the general power cone

  • Henrik A. Friberg
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , ,

    Chandrasekaran and Shah (2017) used the exponential cone to model the second-order cone in demonstration of its modeling capabilities. We simplify and extend this result to general power cones. Article Download View An exponential cone representation of the general power cone

    Recognizing weighted means in geodesic spaces

  • Adrian Lewis
    • Categories Convex Optimization Tags , , , , ,

    Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally whether or not a given point is such an average, exactly or approximately. In nonpositively curved spaces, several averaging notions, including the usual … Read more

    Strict efficiency in set optimization studied with the set approach

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization Tags , , , , ,

    This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the $l$-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms … Read more

    A mathematical introduction to SVMs with self-concordant kernel

  • Florian Jarre
    • Categories Data Science Algorithms, Data-Mining, Quadratic Programming Tags , ,

    A derivation of so-called “soft-margin Support Vector Machines with kernel” is presented which does not rely on concepts from functional analysis such as Mercer’s theorem that is frequently cited in this context, and that leads to a new analysis of the continuity properties of the kernel functions such as a new self-concordance condition for the … Read more

    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

    Robust System Identification: Finite-sample Guarantees and Connection to Regularization

  • Hyuk Park
    • Categories Control Applications, Robust Optimization, Semi-definite Programming Tags , ,

    We address the problem of identifying a stable linear time-invariant system from a single sample trajectory. The least squares estimate (LSE) is a commonly used algorithm for this purpose. However, LSE may exhibit poor identification errors when the number of samples is small. To mitigate the issue, we introduce the robust LSE, which integrates robust … 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