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2014 | OriginalPaper | Chapter

Well-Posedness, Regularization, and Viscosity Solutions of Minimization Problems

Author : D. V. Pai

Published in: Nonlinear Analysis

Publisher: Springer India

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Abstract

This chapter is divided into two parts. The first part surveys some classical notions for well-posedness of minimization problems. The main aim here is to synthesize some known results in approximation theory for best approximants, restricted Chebyshev centers, and prox points from the perspective of well-posedness of these problems. The second part reviews Tikhonov regularization of ill-posed problems. This leads us to revisit the so-called viscosity methods for minimization problems using the modern approach of variational convergence. Lastly, some of these results are particularized to convex minimization problems, and also to ill-posed inverse problems.

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previous chapter Measures of Noncompactness and Well-Posed Minimization Problems

next chapter Best Approximation in Nonlinear Functional Analysis

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Title: Well-Posedness, Regularization, and Viscosity Solutions of Minimization Problems
Author: D. V. Pai
Publisher: Springer India
Book: Nonlinear Analysis
Print ISBN: 978-81-322-1882-1

Electronic ISBN: 978-81-322-1883-8

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-81-322-1883-8_5

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