Name
Abstract | ||
|---|---|---|
Purpose - The purpose of this paper is to solve a global optimization problem raised from industry, named the M-problem, posed in the space L(1) of Lebesgue measurable functions of integrable absolute value. Design/methodology/approach - The paper introduces the new concept of V-dense curve (VDC), a generalization of that of alpha-dense curve, to densify subsets of topological vector spaces not necessarily metrisable. It is proved that the feasible set of the M-problem, namely the subset D of L(1) of all probability functions, is densifiable by VDC provided that L(1) to be endowed with the weak topology. Findings - It is proved that the M-problem, consisting of finding a probability function f of D associated to the mean life of an electronic devise that minimizes the expectation defined by a certain functional on L(1), is not a well-posed problem in D. Nevertheless, by virtue of the compactness, the M-problem has solution on each weak VDC in D for arbitrary weak 0-neighbourhood V, which allows to find an approximate probability function with arbitrary precision. Originality/value - The paper has designed, by means of the VDC-method, a convergent algorithm to find approximate solutions in ill-posed global optimization problems when the feasible set is contained in a non-metrisable topological vector space. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1108/03684920910962605 | KYBERNETES |
Keywords | Field | DocType |
Cybernetics,Optimization techniques,Topology,Vectors | Topology,Vector space,Mathematical optimization,Global optimization,Topological vector space,Measurable function,Compact space,Feasible region,Probability density function,Lebesgue integration,Mathematics | Journal |
Volume | Issue | ISSN |
38 | 5 | 0368-492X |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
1 | ||