Motivation and Overview

  • Hoang Tuy
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 22)


We will be concerned with optimization problems of the general form
$$\min \{ f\left( x \right)|g_i \left( x \right) \leqslant 0\left( {i = 1, \ldots ,m} \right),x \in X\} $$
where X is a closed convex set in R n, f : Ω→ R and g i : Ω→R, i= 1,…,m are functions defined on some set Ω in R n containing X. Denoting the feasible set by S:
$$S = \{ x \in X|g_i \left( x \right) \leqslant 0,i = 1, \ldots ,m\}$$
we can also write the problem as
$$\min \{ f(x)\left| {x \in S\} .} \right.$$


Global Optimization Problem Good Feasible Solution Nonconvex Optimization Problem Concave Minimization Unique Global Minimizer 


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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Hoang Tuy
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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