General Lipschitz Optimization Applying Penalty Multipliers

  • János D. Pintér
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 6)


Consider now the Lipschitzian global optimization problem in the following general form:
$$\begin{array}{*{20}{c}} {\min {{f}_{0}}\left( x \right)} \hfill \\ {x \in D = \left\{ {a \leqslant x \leqslant b:{{f}_{i}}\left( x \right) \leqslant 0,i = 1, \ldots ,I} \right\} \subset \mathbb{R}{{}^{s}}} \hfill \\ \end{array}$$
In accordance with the discussion in Chapter 2.7, we shall assume that D is the closure of a nonempty, bounded, open set in the real n-dimensional space n , and that the constraint functions f i , i = 0,1,..., I, are all Lipschitz-continuous on D, with corresponding Lipschitz-constants L i = L i (D,f i ), i = 0,1,..., I. In other words, the inequalities
$$\left| {{f_i}(x) - {f_i}(y)} \right|{L_i}\left\| {x - y} \right\|$$
are assumed to hold for all pairs of x, y from D.


Subdivision Strategy Penalty Approach Major Iteration Penalty Function Approach Augmented Objective 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • János D. Pintér
    • 1
  1. 1.Pintér Consulting ServicesDalhousie UniversityCanada

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