Nikolaos Sahinidis

Speeding Up Mixed-Integer Programming Solvers with Sparse Learning for Branching

  • Selin Bayramoglu
  • George L. Nemhauser
  • Nikolaos Sahinidis
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms Tags , ,

    Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial computational resources for both training and deployment, typically with GPU parallelization. In this work, we take a different path by developing interpretable models that are … Read more

    New Proofs of Exact LP Reformulations for Binary Polynomial Optimization with Bounded Treewidth

  • Sourabh Kumar Choudhary
  • Santanu S. Dey
  • Nikolaos Sahinidis
    • Categories Combinatorial Optimization Tags , ,

    In this work, we revisit binary polynomial optimization (BPO) problems with limited treewidth of the associated graph. We provide alternate proofs of the exactness of a reformulated linear program (LP) with O(n.2^d) variables, n being the number of variables and d being the treewidth of the associated graph. The first proof relies on expressing any … Read more

    Water network design and operation optimization: Leveraging approximations

  • Sourabh Kumar Choudhary
  • Santanu S. Dey
  • Nikolaos Sahinidis
    • Categories Network Optimization Tags , ,

    This study concerns the optimal design and operation of produced water and urban water networks. The optimization formulations of these problems have inherent nonconvexity, making them hard to solve. We address a key source of nonconvexity and difficulty in solving these problems: the representation of frictional pressure changes across network nodes using nonlinear constraints, typically … Read more

    Nonconvex optimization problems involving the Euclidean norm: Challenges, progress, and opportunities

  • Anatoliy Kuznetsov
  • Nikolaos Sahinidis
    • Categories Global Optimization, Optimization Software Benchmark Tags , , ,

    The field of global optimization has advanced significantly over the past three decades. Yet, the solution of even small instances of many nonconvex optimization problems involving the Euclidean norm to global optimality remains beyond the reach of modern global optimization methods. These problems include numerous well-known and high-impact open research questions from a diverse collection … Read more

    SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs

  • Carlos Nohra
  • Arvind U. Raghunathan
  • Nikolaos Sahinidis
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , , , ,

    We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of … Read more

    Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs

  • Carlos Nohra
  • Arvind U. Raghunathan
  • Nikolaos Sahinidis
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through perturbations of the quadratic matrix. We investigate the theoretical properties of these quadratic relaxations and show that they are equivalent to some particular semidefinite programs. … Read more

    On the impact of running intersection inequalities for globally solving polynomial optimization problems

  • Alberto Del Pia
  • Aida Khajavirad
  • Nikolaos Sahinidis
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Global Optimization Theory

    We consider global optimization of nonconvex problems whose factorable reformulations contain a collection of multilinear equations. Important special cases include multilinear and polynomial optimization problems. The multilinear polytope is the convex hull of a set of binary points satisfying a number of multilinear equations. Running intersection inequalities are a family of facet-defining inequalities for the … Read more

    QPLIB: A Library of Quadratic Programming Instances

  • Pietro Belotti
  • Antonio Frangioni
  • Fabio Furini
  • Ambros Gleixner
  • Nicholas I. M. Gould
  • Leo Liberti
  • Andrea Lodi
  • Hans D Mittelmann
  • Ruth Misener
  • Nikolaos Sahinidis
  • Emiliano Traversi
  • Stefan Vigerske
  • Angelika Wiegele
    • Categories Quadratic Programming

    This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very “varied” class of problems, comprising sub-classes of problems ranging from trivial to undecidable. Solution methods for QP are very diverse, ranging … Read more