ISSN:
1573-2878
Keywords:
Nonlinear programming problems
;
pseudomonotonic functions
;
Kuhn-Tucker conditions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we consider the following nonlinear programming problem: $$max[min]\{ f(x) = (c^T \cdot x + c_0 )/(d^T \cdot x + d_0 )|x \in L\} ,$$ in the feasible region $$L = \{ x \in R^n |A \cdot x = b,l(x) \leqslant 0\} ;$$ here,c andd are vectors ofR n ;c 0,d 0 are real constants;A is anm×n matrix of rankm; b is a vector ofR m ;l(x)=0 is the equation of a bounded hypersurface inR n . We assume thatd T·x+d 0≠0 in L. We study the case where $$l(x) = |x - e|^2 - r^2 ,$$ wherer≠0 ande is the vector with all the components equal to 1. We obtain a simple explicit solution, and we illustrate the resulting algorithm.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192122
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