Agarwal, R. P. (ed.), Recent trends in optimization theory and applications. Singapore: World Scientific. World Sci. Ser. Appl. Anal. 5, 79-106 (1995).

The authors present a method of solving the constrained extremum problem through converting it into separating of the sets in the image space. The problem is formulated as the generalized system

$F(x,y)\in \mathscr{H}\subset {\mathbb{R}}^{\nu},\phantom{\rule{4pt}{0ex}}x\in K\subseteq H,\phantom{\rule{4pt}{0ex}}y\in Y$ with a cone

$\mathscr{H},\phantom{\rule{4pt}{0ex}}H$ a real Hilbert space,

$Y$ a parameter set. The impossibility of a generalized system means the condition

$\mathscr{H}\cap {\mathcal{K}}_{y}=\varnothing $, where

${\mathcal{K}}_{y}:=F(K,y)$ is the image of

$K$ at

$y\xb7$ The main problem reduced to impossibility is:

$minf\left(x\right)$ subject to

$x\in R:=\{x\in K:g(x)\in \mathcal{C}\}$ with a convex and closed cone

$\mathcal{C}\subset {\mathbb{R}}^{m}\xb7$ Applications to variational and quasivariational inequalities are shown. Results concerned with optimality conditions, saddle points, Lagrange multipliers, penalty method are presented, too.