perspective reformulation

Automatic Reformulations for Convex Mixed-Integer Nonlinear Optimization: Perspective and Separability

  • Meenarli Sharma
  • Ashutosh Mahajan
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems Tags , , , ,

    Tight reformulations of combinatorial optimization problems like Convex Mixed-Integer Nonlinear Programs (MINLPs) enable one to solve these problems faster by obtaining tight bounds on the optimal value. We consider two techniques for reformulation: perspective reformulation and separability detection. We develop routines for the automatic detection of problem structures suitable for these reformulations and implement new … Read more

    Projective Cutting Planes for General QP with Indicator Constraints

  • Ulf Friedrich
  • Dennis Kreber
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    General quadratic optimization problems with linear constraints and additional indicator constraints on the variables are studied. Based on the well-known perspective reformulation for mixed-integer quadratic optimization problems, projective cuts are introduced as new valid inequalities for the general problem. The key idea behind the theory of these cutting planes is the projection of the continuous … Read more

    Marketing Mix Optimization with Practical Constraints

  • Hsin-Chan Huang
  • Alvin Lim
  • Jiefeng Xu
    • Categories (Mixed) Integer Nonlinear Programming, Marketing, Second-Order Cone Programming Tags , , , , , ,

    In this paper, we address a variant of the marketing mix optimization (MMO) problem which is commonly encountered in many industries, e.g., retail and consumer packaged goods (CPG) industries. This problem requires the spend for each marketing activity, if adjusted, be changed by a non-negligible degree (minimum change) and also the total number of activities … Read more

    Ideal formulations for constrained convex optimization problems with indicator variables.

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

    Motivated by modern regression applications, in this paper, we study the convexification of a class of convex 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 non-separable objective, indicator variables, and combinatorial constraints. Specifically, we give … Read more

    Safe screening rules for L0-Regression

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , ,

    We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. … Read more