Normed vector space X

Legendre-Fenchel duality plays a helpful role in convex optimization. Herein, we introduce some overview of Legendre-Fenchel duality, with an eye toward later applications in nonlinear elasticity. The basic tool here is functional analysis.

3p viputrajaya2711 22-06-2020 14 0   Download

Hilbert Spaces 1.1 Inner product spaces Example 1.1 Prove that in a real vector space with inner product we have (x, y) = 1 4 x + y2 − x − y2, and in a complex vector space with inner product we have (x, y) = 1 4 x + y2 − x − y2 + i x + iy2 + i x − iy2. These are the so-called polarization identities. They tell us that in a Hilbert space, the inner product is determined by the norm.

109p sn_buon 29-11-2012 51 4   Download