superadditivity

Theorems of the Alternative for Conic Integer Programming

  • Temitayo Ajayi
  • Andrew J. Schaefer
  • Varun Suriyanarayana
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Farkas’ Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested … Read more

    Lifting 2-integer knapsack inequalities

  • Agostinho Agra
  • Miguel Constantino
    • Categories Integer Programming Tags , ,

    In this paper we discuss the generation of strong valid inequalities for (mixed) integer knapsack sets based on lifting of valid inequalities for basic knapsack sets with two integer variables (and one continuous variable). The description of the basic polyhedra can be made in polynomial time. We use superadditive valid functions in order to obtain … Read more