Minimisation of Convex Functions and Variational Inequalities
11 Abril 2019, 14:30 • José Francisco da Silva Costa Rodrigues
Minimisation of Convex Functions in reflexive Banach spaces—the direct method in the bonded case and in the coercive case. Characterisation of the solutions under (Gâteaux) differentiability conditions and in the general subdifferential case. Variational inequalities and the Minty trick. Proximity mappings in Hilbert spaces. The case of a bilinear symmetric form. The finite dimension approximation method of the existence of solutions of certain variational inequalities for monotone, coercive operators with different types of weak continuities: semi-continuous, demicontinuos and weakly continuous over the subspaces of finite dimension. Extension to pseudo-monotone operators. Chap. 2 of [ET].Further readings:
Brezis, Haïm Équations et inéquations non linéaires dans les espaces vectoriels en dualité. (French)
Ann. Inst. Fourier (Grenoble)
18 1968 fasc. 1, 115–175.
http://www.numdam.org/item/?id=AIF_1968__18_1_115_0
Chapter 2 of Tomáš Roubíek, Nonlinear Partial Differential Equations with Applications, Birkhauser, 2013