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On existence of solutions to degenerate nonlinear optimization problems

Agnieszka Prusińska, Alexey Tret'yakov (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate the existence of the solution to the following problem min φ(x) subject to G(x)=0, where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.

On Kato non-singularity

Robin Harte (1996)

Studia Mathematica

An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.

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