Connections between Nonlinear Programming and Discrete Optimization

Franco Giannessi () and Fabio Tardella ()
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Franco Giannessi: Università di Pisa, Department of Mathematics
Fabio Tardella: University of Rome “La Sapienza”, Department of Mathematics Faculty of Economics

A chapter in Handbook of Combinatorial Optimization, 1998, pp 149-188 from Springer

Abstract: 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.

Keywords: Voronoi Diagram; Nonlinear Program; Discrete Optimization; Discrete Optimization Problem; Minimax Problem (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4613-0303-9_3

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