convex optimization

Superiorization vs. Accelerated Convex Optimization: The Superiorized/Regularized Least-Squares Case

  • Yair Censor
  • Stefania Petra
  • Christoph Schnörr
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

    In this paper we conduct a study of both superiorization and optimization approaches for the reconstruction problem of superiorized/regularized solutions to underdetermined systems of linear equations with nonnegativity variable bounds. Specifically, we study a (smoothed) total variation regularized least-squares problem with nonnegativity constraints. We consider two approaches: (a) a superiorization approach that, in contrast to … Read more

    Understanding Limitation of Two Symmetrized Orders by Worst-case Complexity

  • Ruoyu Sun
  • Zhisheng Xiao
  • Peijun Xiao
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    It was recently found that the standard version of multi-block cyclic ADMM diverges. Interestingly, Gaussian Back Substitution ADMM (GBS-ADMM) and symmetric Gauss-Seidel ADMM (sGS-ADMM) do not have the divergence issue. Therefore, it seems that symmetrization can improve the performance of the classical cyclic order. In another recent work, cyclic CD (Coordinate Descent) was shown to … Read more

    Domain-Driven Solver (DDS): a MATLAB-based Software Package for Convex Optimization Problems in Domain-Driven Form

  • Mehdi Karimi
  • Levent Tunçel
    • Categories Convex and Nonsmooth Optimization, Optimization Software and Modeling Systems Tags , , , ,

    Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [11]. The current version of DDS accepts every combination of the following function/set constraints: (1) symmetric cones (LP, SOCP, and SDP); (2) quadratic constraints; (3) direct sums of an arbitrary collection of 2-dimensional convex sets defined as the epigraphs of … Read more

    A family of multi-parameterized proximal point algorithms

  • Jianchao Bai
  • Ke Guo
  • Xiaokai Chang
    • Categories Convex Optimization Tags , , ,

    In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective of variational inequality. Preliminary numerical experiments on testing a sparse minimization problem from signal processing indicate that the proposed … Read more

    Optimal K-Thresholding Algorithms for Sparse Optimization Problems

  • Yun-Bin Zhao
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Data-Mining Tags , , , , ,

    The simulations indicate that the existing hard thresholding technique independent of the residual function may cause a dramatic increase or numerical oscillation of the residual. This inherit drawback of the hard thresholding renders the traditional thresholding algorithms unstable and thus generally inefficient for solving practical sparse optimization problems. How to overcome this weakness and develop … Read more

    Indefinite linearized augmented Lagrangian method for convex programming with linear inequality constraints

  • Bingsheng He
  • Shengjie Xu
  • Jing Yuan
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , , , ,

    The augmented Lagrangian method (ALM) is a benchmark for tackling the convex optimization problem with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literatures. However, much less attention has been paid to ALM for efficiently solving the linearly inequality-constrained convex minimization model. In this paper, … Read more

    General risk measures for robust machine learning

  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Henri Gérard
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , , , ,

    A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often estimated from training sets, which may lead to poor out-of-sample performance. In this work, we … Read more

    Tractable semi-algebraic approximation using Christoffel-Darboux kernel

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Swann Marx
  • Edouard Pauwels
  • Tillmann Weisser
    • Categories Semi-definite Programming Tags , , , ,

    We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the graph of the function. Such an input is available when approximating weak (or measure-valued) solution of optimal control problems, entropy … Read more

    CONICOPF: Conic relaxations for AC optimal power flow computations

  • Christian Bingane
  • Miguel F. Anjos
  • Sébastien Le Digabel
    • Categories Semi-definite Programming Tags , , ,

    Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite relaxations for large-scale meshed networks in terms of optimality gap and computation time: the tight-and-cheap relaxation (TCR) and the quadratic convex relaxation … Read more

    Status Determination by Interior-Point Methods for Convex Optimization Problems in Domain-Driven Form

  • Mehdi Karimi
  • Levent Tunçel
    • Categories Convex Optimization Tags , , , ,

    We study the geometry of convex optimization problems given in a Domain-Driven form and categorize possible statuses of these problems using duality theory. Our duality theory for the Domain-Driven form, which accepts both conic and non-conic constraints, lets us determine and certify statuses of a problem as rigorously as the best approaches for conic formulations … Read more