quadratic programming

A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming

  • David Ek
  • Anders Forsgren
    • Categories Quadratic Programming Tags , , , ,

    The focus in this work is interior-point methods for quadratic optimization problems with linear inequality constraints where the system of nonlinear equations that arise are solved with Newton-like methods. In particular, the concern is the system of linear equations to be solved at each iteration. Newton systems give high quality solutions but there is an … Read more

    On the Complexity of Finding a Local Minimizer of a Quadratic Function over a Polytope

  • Amir Ali Ahmadi
  • Jeffrey Zhang
    • Categories Quadratic Programming Tags , , ,

    We show that unless P=NP, there cannot be a polynomial-time algorithm that finds a point within Euclidean distance $c^n$ (for any constant $c \ge 0$) of a local minimizer of an $n$-variate quadratic function over a polytope. This result (even with $c=0$) answers a question of Pardalos and Vavasis that appeared in 1992 on a … Read more

    On the convexification of constrained quadratic optimization problems with indicator variables

  • Andrés Gómez
  • Simge Küçükyavuz
  • Linchuan Wei
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , ,

    Motivated by modern regression applications, in this paper, we study the convexification of quadratic optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work on convexification of sparse regression problems, we simultaneously consider the nonlinear objective, indicator variables, and combinatorial constraints. We prove that for a separable quadratic … Read more

    Outer Approximation for Global Optimization of Mixed-Integer Quadratic Bilevel Problems

  • Veronika Grimm
  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , ,

    Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel problems and the most recent algorithms use branch-and-cut techniques from mixed-integer programming that are especially tailored for the bilevel context. In this paper, we consider MIQP-QP … Read more

    Single Allocation Hub Location with Heterogeneous Economies of Scale

  • Okan Arslan
  • Masoud Chitsaz
  • Gilbert Laporte
  • Andrea Lodi
  • Borzou Rostami
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Combinatorial Optimization Tags , , , , ,

    We study the single allocation hub location problem with heterogeneous economies of scale (SAHLP-h). The SAHLP-h is a generalization of the classical single allocation hub location problem (SAHLP), in which the hub-hub connection costs are piecewise linear functions of the amounts of flow. We model the problem as an integer non-linear program, which we then … Read more

    An algorithm for optimization with disjoint linear constraints and its application for predicting rain

  • Tijana Janjic
  • Philippe L. Toint
  • Yvonne Ruckstuhl
    • Categories Basic Sciences Applications, Quadratic Programming Tags ,

    A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables in a different subset are constrained to remain in a convex set. The proposed algorithm exploits the structure by combining steps … Read more

    On the asymptotic convergence and acceleration of gradient methods

  • Yu-Hong Dai
  • Yakui Huang
  • Xin-Wei Liu
  • Hongchao Zhang
    • Categories Convex Optimization, Quadratic Programming, Unconstrained Optimization Tags , , , , , ,

    We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate … Read more

    Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

  • Alper Atamturk
  • Carlos Deck
  • Hyemin Jeon
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , , , ,

    The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic models are solved efficiently over convex sets, their discrete counterparts are intractable. In this paper, we give a highly effective successive quadratic upper-bounding procedure … Read more

    Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks

  • Radu Baltean-Lugojan
  • Pierre Bonami
  • Ruth Misener
  • Andrea Tramontani
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming Tags , , , , ,

    Semidefinite programming relaxations complement polyhedral relaxations for quadratic optimization, but global optimization solvers built on polyhedral relaxations cannot fully exploit this advantage. This paper develops linear outer-approximations of semidefinite constraints that can be effectively integrated into global solvers. The difference from previous work is that our proposed cuts are (i) sparser with respect to the … Read more