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

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Nonlinear Analysis

Part of the book series: Trends in Mathematics ((TM))

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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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Authors and Affiliations

  1. Indian Institute of Technology Gandhinagar, VGEC Campus, Visat-Gandhinagar Highway, Chandkheda, 382424, Ahmedabad, India

    D. V. Pai

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Correspondence to D. V. Pai .

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  1. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Qamrul Hasan Ansari

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Pai, D.V. (2014). Well-Posedness, Regularization, and Viscosity Solutions of Minimization Problems. In: Ansari, Q. (eds) Nonlinear Analysis. Trends in Mathematics. Birkhäuser, New Delhi. https://doi.org/10.1007/978-81-322-1883-8_5

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