Optimization of Singular Values of Parameter Dependent Matrices using Hybrid Algorithms

This article considers extremal problems for singular spectrum components of real-valued matrices depending on parameters. Criterion functions are supposed to be continuous, Lipschitzian, multiextremal and not necessarily differentiable. While searching for global solutions we used new hybrid algorithms that combine a stochastic algorithm for scanning a search space and deterministic methods for local search. The first hybrid algorithm determines local solutions using the linearization method with smoothing approximations. The second algorithm does it by using the modified space-filling curve method. Our work provides numerical examples.

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