Univariate Algorithms for Solving Global Optimization Problems with Multiextremal Non-differentiable Constraints
In this chapter, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal and non-differentiable are considered. The constrained problem is reduced to a discontinuous unconstrained problem by the index scheme without introducing additional parameters or variables. It is shown that the index approach proposed by R.G. Strongin for solving these problems in the framework of stochastic information algorithms can be successfully extended to geometric algorithms constructing non-differentiable discontinuous minorants for the reduced problem. A new geometric method using adaptive estimates of Lipschitz constants is described and its convergence conditions are established. Numerical experiments including comparison of the new algorithm with methods using penalty approach are presented.
Key wordsGlobal optimization multiextremal constraints geometric algorithms index scheme
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