Variational Methods and Optimization

Hemant Kumar Pathak ()
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Hemant Kumar Pathak: Pandit Ravishankar Shukla University, School of Studies in Mathematics

Chapter Chapter 7 in An Introduction to Nonlinear Analysis and Fixed Point Theory, 2018, pp 513-606 from Springer

Abstract: Abstract The purpose of this chapter is to give an introduction of variational methods and optimization theory in a rather convincing manner along with results of nonlinear analysis leading to an applied environment. So, we have chosen variational principles as the starting point of our discussion in the framework of Banach space theory that leads to optimization with the observation that by applying the techniques involved in variational methods and optimization one can deal with some real-world problems that arise in nonlinear analysis. We initiate our discussion by presenting some variational principles and their applications. The epicenter of our discussion is the so-called Ekeland variational principle (in short, EVP). Indeed, we show that EVP is equivalent to some other well-known results of nonlinear analysis, notably Takahashi’s minimization theorem.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-8866-7_7

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DOI: 10.1007/978-981-10-8866-7_7

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