(Mixed) Integer Nonlinear Programming

Compact Disjunctive Approximations to Nonconvex Quadratically Constrained Programs

  • Hongbo Dong
  • Yunqi Luo
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Second-Order Cone Programming

    Decades of advances in mixed-integer linear programming (MILP) and recent development in mixed-integer second-order-cone programming (MISOCP) have translated very mildly to progresses in global solving nonconvex mixed-integer quadratically constrained programs (MIQCP). In this paper we propose a new approach, namely Compact Disjunctive Approximation (CDA), to approximate nonconvex MIQCP to arbitrary precision by convex MIQCPs, which … Read more

    Submodularity and valid inequalities in nonlinear optimization with indicator variables

  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    We propose a new class of valid inequalities for mixed-integer nonlinear optimization problems with indicator variables. The inequalities are obtained by lifting polymatroid inequalities in the space of the 0–1 variables into conic inequalities in the original space of variables. The proposed inequalities are shown to describe the convex hull of the set under study … Read more

    A new combinatorial algorithm for separable convex resource allocation with nested bound constraints

  • Qie He
  • Kameng Nip
  • Zeyang Wu
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization Tags , , ,

    The separable convex resource allocation problem with nested bound constraints aims to allocate $B$ units of resources to $n$ activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve … Read more

    A convex integer programming approach for optimal sparse PCA

  • Santanu S. Dey
  • Rahul Mazumder
  • Guanyi Wang
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming

    Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in scientific data analysis. The PCA direction, given by the leading eigenvector of a covariance matrix, is a linear combination of all features with nonzero loadings—this impedes interpretability. Sparse principal component analysis (SPCA) is a framework that enhances interpretability by incorporating … Read more

    Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning

  • Mirjam Ambrosius
  • Veronika Grimm
  • Thomas Kleinert
  • Frauke Liers
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the … Read more

    Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP

  • Lena C. Altherr
  • Marc E. Pfetsch
  • Andreas Schmitt
  • Philipp Leise
    • Categories (Mixed) Integer Nonlinear Programming, Mechanical Engineering, Robust Optimization Tags , , , , , , ,

    Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goal of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in … Read more

    A Branch-and-Cut Algorithm for Solving Mixed-integer Semidefinite Optimization Problems

  • Ken Kobayashi
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Semi-definite Programming Tags , , ,

    This paper is concerned with a cutting-plane algorithm for solving mixed-integer semidefinite optimization (MISDO) problems. In this algorithm, the positive semidefinite constraint is relaxed, and the resultant mixed-integer linear optimization problem is repeatedly solved with valid inequalities for the relaxed constraint. We prove convergence properties of the algorithm. Moreover, to speed up the computation, we … Read more

    On robust fractional 0-1 programming

  • Colin Gillen
  • Andrés Gómez
  • Oleg A. Prokopyev
  • Erfan Mehmanchi
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , ,

    We study single- and multiple-ratio robust fractional 0-1 programming problems (RFPs). In particular, this work considers RFPs under a wide-range of disjoint and joint uncertainty sets, where the former implies separate uncertainty sets for each numerator and denominator, and the latter accounts for different forms of inter-relatedness between them. First, we demonstrate that, unlike the … Read more

    Location and Capacity Planning of Facilities with General Service-Time Distributions Using Conic Optimization

  • Ahmadi-Javid Amir
  • Oded Berman
  • Pooya Hoseinpour
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Facility Planning and Design

    This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. … Read more

    A mixed-integer fractional optimization approach to best subset selection

  • Andrés Gómez
  • Oleg A. Prokopyev
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Statistics Tags , , ,

    We consider the best subset selection problem in linear regression, i.e., finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We show that, for a broad range of criteria used in the statistics literature, the best subset selection problem can be modeled as … Read more