Convex and Nonsmooth Optimization

Dini Derivative and a Characterization for Lipschitz and Convex Functions on Riemannian Manifolds

  • Orizon Pereira Ferreira
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , ,

    Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given. Article Download View Dini Derivative and a Characterization for Lipschitz and Convex Functions on Riemannian … Read more

    Consistency of robust portfolio estimators

  • Katrin Schöttle
  • Ralf Werner
    • Categories Convex Optimization, Finance and Economics, Statistics Tags ,

    It is a matter of common knowledge that traditional Markowitz optimization based on sample means and covariances performs poorly in practice. For this reason, diverse attempts were made to improve performance of portfolio optimization. In this paper, we investigate three popular portfolio selection models built upon classical mean-variance theory. The first model is an extension … Read more

    Simplex-type algorithm for optimizing a pseudolinear quadratic fractional function over a polytope

  • Miklós Ujvári
    • Categories Constrained Nonlinear Optimization, Generalized Convexity/Monoticity

    Recently Cambini and Carosi described a characterization of pseudolinearity of quadratic fractional functions. A reformulation of their result was given by Rapcsák. Using this reformulation, in this paper we describe an alternative proof of the Cambini–Carosi Theorem. Our proof is shorter than the proof given by Cambini–Carosi and less involved than the proof given by … Read more

    A New Class of Interior Proximal Methods for Optimization over the Positive Orthant

  • Paulo Roberto Oliveira
  • Sissy da S. Souza
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    In this work we present a family of variable metric interior proximal methods for solving optimization problems under nonnegativity constraints. We define two algorithms, in the inexact and exact forms. The kernels are metrics generated by diagonal matrices in each iteration and the regularization parameters are conveniently chosen to force the iterates to be interior … Read more

    Metric regularity and systems of generalized equations

  • Andrei V. Dmitruk
  • Alexander Y. Kruger
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , ,

    The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version … Read more

    Large Scale Portfolio Optimization with Piecewise Linear Transaction Costs

  • Potaptchik Marina
  • Levent Tunçel
  • Henry Wolkowicz
    • Categories Finance and Economics, Nonsmooth Optimization, Quadratic Programming Tags , , ,

    We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model of the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle … Read more

    PROXIMAL THRESHOLDING ALGORITHM FOR MINIMIZATION OVER ORTHONORMAL BASES

  • Patrick L. Combettes
  • Jean-Christophe Pesquet
    • Categories Convex Optimization, Infinite Dimensional Optimization, Unconstrained Optimization Tags , , ,

    The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing in particular several characterizations of … Read more

    Geometric Dual Formulation for First-derivative-based Univariate Cubic $ Splines

  • S.C. Fang
  • Yun-Bin Zhao
  • J.E. Lavery
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based ${\cal C}^1$-smooth univariate cubic $L_1$ splines. An $L_1$ spline minimizes the $L_1$ norm of the difference between the first-order derivative of the spline and the local divided difference of … Read more

    An efficient method to compute traffic assignment problems with elastic demands

  • Frédéric Babonneau
  • Jean-Philippe Vial
    • Categories Convex Optimization, Transportation Tags , ,

    The traffic assignment problem with elastic demands can be formulated as an optimization problem, whose objective is sum of a congestion function and a disutility function. We propose to use a variant of the Analytic Center Cutting Plane Method to solve this problem. We test the method on instances with different congestion functions (linear with … Read more

    A Proximal Point Algorithm with phi-Divergence to Quasiconvex Programming

  • F. G. M. Cunha
    • Categories Generalized Convexity/Monoticity, Nonlinear Optimization Tags , ,

    We use the proximal point method with the phi-divergence given by phi(t) = t – log t – 1 for the minimization of quasiconvex functions subject to nonnegativity constraints. We establish that the sequence generated by our algorithm is well-defined in the sense that it exists and it is not cyclical. Without any assumption of … Read more