Nonlinear Optimization

Complementarity-Based Nonlinear Programming Techniques for Optimal Mixing in Gas Networks

  • Falk M. Hante
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , ,

    We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we … Read more

    A General Regularized Continuous Formulation for the Maximum Clique Problem

  • James T. Hungerford
  • Francesco Rinaldi
    • Categories Combinatorial Optimization, Network Optimization, Nonlinear Optimization Tags , , , ,

    In this paper, we develop a general regularization-based continuous optimization framework for the maximum clique problem. In particular, we consider a broad class of regularization terms that can be included in the classic Motzkin-Strauss formulation and we develop conditions that guarantee the equivalence between the continuous regularized problem and the original one in both a … Read more

    A sequential optimality condition related to the quasinormality constraint qualification and its algorithmic consequences

  • Roberto Andreani
  • N. S. Fazzio
  • María Laura Schuverdt
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In the present paper, we prove that the augmented Lagrangian method converges to KKT points under the quasinormality constraint qualification, which is associated with the external penalty theory. For this purpose, a new sequential optimality condition for smooth constrained optimization, called PAKKT, is defined. The new condition takes into account the sign of the dual … Read more

    Planar Maximum Coverage Location Problem with Partial Coverage and General Spatial Representation of Demand and Service Zones

  • Manish Bansal
    • Categories Approximation Algorithms, Nonlinear Optimization, Production and Logistics

    We introduce a new generalization of the classical planar maximum coverage location problem (PMCLP) in which demand zones and service zone of each facility are represented by spatial objects such as circles, polygons, etc., and are allowed to be located anywhere in a continuous plane. In addition, we allow partial coverage in its true sense, … Read more

    On Affine Invariant Descent Directions

  • Yu-Hong Dai
  • Florian Jarre
  • Felix Lieder
    • Categories Nonlinear Optimization Tags , ,

    This paper explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions $f$ at a given point, it is shown that for quadratic functions there exists exactly one invariant descent direction in the strictly convex case and generally none in the nondegenerate … Read more

    Portfolio Optimization with Entropic Value-at-Risk

  • Ahmadi-Javid Amir
  • Fallah-Tafti Malihe
    • Categories Constrained Nonlinear Optimization, Finance and Economics, Stochastic Programming

    The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, while well-known monotone risk measures, such as VaR and … Read more

    The Trimmed Lasso: Sparsity and Robustness

  • Dimitris Bertsimas
  • Rahul Mazumder
  • Martin Copenhaver
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Statistics

    Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing … Read more

    On types of degenerate critical points of real polynomial functions

  • Feng Guo
  • Tiên-So'n Pham
    • Categories Unconstrained Optimization Tags , , , ,

    In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point $c$, which is degenerate, of a multivariate polynomial function $f$. To this end, we introduce the definition of faithful radius of $c$ by means of the curve of tangency of $f$. … Read more

    Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Nonlinear Optimization Tags ,

    The unconstrained minimization of a sufficiently smooth objective function $f(x)$ is considered, for which derivatives up to order $p$, $p\geq 2$, are assumed to be available. An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order $p$ and that is guaranteed to find a first- and second-order critical point in … Read more

    Glider Routing and Trajectory Optimisation in Disaster Assessment

  • Maria Battarra
  • Jörg Fliege
  • W.P. Coutinho
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Systems governed by Differential Equations Optimization

    In this paper, we introduce the Glider Routing and Trajectory Optimisation Problem (GRTOP), the problem of finding simultaneously optimal routes and trajectories for a fleet of gliders with the aim of surveying a set of locations. We propose a novel Mixed-Integer Nonlinear Programming (MINLP) formulation for the GRTOP, which simultaneously optimises the routes as well … Read more