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Connections between Nonlinear Programming and Discrete Optimization

In: Handbook of Combinatorial Optimization

Author

Listed:
  • Franco Giannessi

    (Università di Pisa, Department of Mathematics)

  • Fabio Tardella

    (University of Rome “La Sapienza”, Department of Mathematics Faculty of Economics)

Abstract

Given a set X,a function f: X→ℝ and a subset S of X –we consider the problem: 1 $$\min f(x)s.t.x \in S$$ 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.

Suggested Citation

  • Franco Giannessi & Fabio Tardella, 1998. "Connections between Nonlinear Programming and Discrete Optimization," Springer Books, in: Ding-Zhu Du & Panos M. Pardalos (ed.), Handbook of Combinatorial Optimization, pages 149-188, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0303-9_3
    DOI: 10.1007/978-1-4613-0303-9_3
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