Summary
the 2014 International Symposium on Nonlinear Theory and its Applications
2014
Session Number:D1L-C
Session:
Number:D1L-C2
Conditions and estimation of the number of optimal solutions in nonlinear continuous optimization problems
Hideo KANEMITSU,
pp.684-687
Publication Date:2014/9/14
Online ISSN:2188-5079
Summary:
We show more simpler representations of optimal solutions using level set and two conditions for an unconstrained optimization problem: 1) a necessary and sufficient optimality for a Morse function and 2) an existence condition of an optimal solution for a polynomial objective function. We also estimate the number of solutions for the following two kinds of objective functions: 1) univariate polynomial functions and 2) separable functions.