Akshay Gupte

Spatial branch-and-bound for nonconvex separable piecewise linear optimization

  • Thomas Hübner
  • Akshay Gupte
  • Steffen Rebennack
    • Categories (Mixed) Integer Linear Programming, Global Optimization Tags , , , ,

    Nonconvex separable piecewise linear functions (PLFs) frequently appear in applications and to approximate nonlinearitites. The standard practice to formulate nonconvex PLFs is from the perspective of discrete optimisation, using special ordered sets and mixed integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and present a spatial branch-and-bound algorithm (sBB) … Read more

    Edge expansion of a graph: SDP-based computational strategies

  • Akshay Gupte
  • Melanie Siebenhofer
  • Angelika Wiegele
    • Categories Combinatorial Optimization, Parallel Algorithms, Semi-definite Programming Tags , , , ,

    Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant for any graph. The first variant uses the SDP relax- ation first to reduce the search space considerably. One … Read more

    Stochastic programming for an integrated assignment, routing, and scheduling problem

  • Syu-Ning Johnn
  • Andrés Miniguano-Trujillo
  • Yiran Zhu
  • Akshay Gupte
  • Joerg Kalcsics
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Stochastic Programming Tags , , ,

    We study a two-stage stochastic combinatorial optimization problem that integrates fleet-sizing, assignment, routing, and scheduling problems. Although this problem has wide applicability, it arises in particular in the home healthcare industry where a service team of caregivers have to be assigned to patients and put in vehicle fleet that have to be routed amongst the … Read more

    Superadditive duality and convex hulls for mixed-integer conic optimization

  • Akshay Gupte
  • Temitayo Ajayi
  • Amin Khademi
  • Andrew J. Schaefer
    • Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Cutting Plane Approaches Tags , , ,

    We present an infinite family of linear valid inequalities for a mixed-integer conic program, and prove that these inequalities describe the convex hull of the feasible set when this set is bounded and described by integral data. The main element of our proof is to establish a new strong superadditive dual for mixed-integer conic programming … Read more

    Large independent sets in Markov random graphs

  • Akshay Gupte
  • Yiran Zhu
    • Categories Combinatorial Optimization, Graphs and Matroids

    \(\) Computing the maximum size of an independent set in a graph is a famously hard combinatorial problem that has been well-studied for various classes of graphs. When it comes to random graphs, only the classical binomial random graph \(G_{n,p}\) has been analysed and shown to have largest independent sets of size \(\Theta(\log{n})\) w.h.p. This … Read more

    Ordering integers under different permutations

  • Akshay Gupte
    • Categories Approximation Algorithms, Combinatorial Optimization Tags , , , ,

    \(\) The question of finding the largest integer contained between two given lists of integers is trivial when integer ordering is interpreted in its usual way. We propose a nontrivial variant wherein each ordering comparison is performed after integers have been mapped under some bijection, and analyze the computational complexity of our combinatorial problem under … Read more

    Multilinear formulations for computing Nash equilibrium of multi-player matrix games

  • Akshay Gupte
    • Categories (Mixed) Integer Nonlinear Programming, Game Theory, Global Optimization Applications Tags , , , ,

    We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player strategic-form games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended … Read more

    Solving the Home Service Assignment, Routing, and Appointment Scheduling (H-SARA) problem with Uncertainties

  • Syu-Ning Johnn
  • Yiran Zhu
  • Andrés Miniguano-Trujillo
  • Akshay Gupte
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , ,

    The Home Service Assignment, Routing, and Appointment scheduling (H-SARA) problem integrates the strategical fleet-sizing, tactical assignment, operational vehicle routing and scheduling subproblems at different decision levels, with a single period planning horizon and uncertainty (stochasticity) from the service duration, travel time, and customer cancellation rate. We propose a two-stage stochastic mixed-integer linear programming model for … Read more

    Polyhedral Analysis of Symmetric Multilinear Polynomials over Box Constraints

  • Warren Adams
  • Akshay Gupte
  • Yibo Xu
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Polyhedra Tags , , , ,

    It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification question for multilinear polynomials that are symmetric with respect to permutations of variables. Such a permutation-invariant structure naturally implies a quadratic-sized … Read more

    On strong duality, theorems of the alternative, and projections in conic optimization

  • Temitayo Ajayi
  • Akshay Gupte
  • Amin Khademi
  • Andrew J. Schaefer
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    A conic program is the problem of optimizing a linear function over a closed convex cone intersected with an affine preimage of another cone. We analyse three constraint qualifications, namely a Closedness CQ, Slater CQ, and Boundedness CQ (also called Clark- Duffin theorem), that are sufficient for achieving strong duality and show that the first … Read more