Connections between Nonlinear Programming and Discrete Optimization

  • Franco Giannessi
  • Fabio Tardella
Chapter

Abstract

Given a set X,a function f: X→ℝ and a subset S of X we consider the problem:
$$\min f(x)s.t.x \in S$$
(1)
Problem (1) is usually called a combinatorial optimization problem when S is finite and a discrete optimization problem when the points of S are isolated in some topology, i.e., every point of S has a neighbourhood which does not contain other points of S. Obviously, all combinatorial optimization problems are also discrete optimization problems but the converse is not true. A simple example is the problem of minimizing a function on the set of integer points contained in an unbounded polyhedron.

Keywords

Manifold Hull Dition Dinate Rosen 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Franco Giannessi
    • 1
  • Fabio Tardella
    • 2
  1. 1.Department of MathematicsUniversità di PisaPisaItaly
  2. 2.Department of Mathematics Faculty of EconomicsUniversity of Rome “La Sapienza”RomaItaly

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