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submodular optimization

Polyhedral results for a class of cardinality constrained submodular minimization problems

Published: 2014/08/29
  • Shabbir Ahmed
  • Jiajin Yu
  • Categories (Mixed) Integer Linear Programming, 0-1 Programming, Cutting Plane Approaches Tags integer programming, polyhedral theory, submodular optimization

    Motivated by concave cost combinatorial optimization problems, we study the following mixed integer nonlinear set: P = {(w,x) : w >= f(a’x), e’x

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    Keywords

    alternating direction method of multipliers approximation algorithms augmented lagrangian method bilevel optimization Branch-and-Bound branch-and-cut chance constraints column generation combinatorial optimization complexity compressed sensing conic optimization convex optimization cutting planes decomposition derivative-free optimization distributionally robust optimization duality dynamic programming first-order methods global convergence global optimization heuristics integer programming interior point methods large-scale optimization linear programming machine learning mixed-integer linear programming mixed-integer nonlinear programming mixed-integer programming nonconvex optimization nonlinear optimization nonlinear programming nonsmooth optimization optimal control optimization proximal point algorithm quadratic programming robust optimization semidefinite programming stochastic optimization stochastic programming trust-region methods unconstrained optimization

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