Event № 203
The Legendre transform (LET) is a product of a general duality principle: any smooth curve is, on the one hand, a locus of pairs which satisfy the given equation, and on the other, an envelope of a family of its tangent lines. An application of the LET to a strictly convex and smooth function leads to the Legendre identity (LEID). For strictly convex and three times differentiable functions, the LET leads to the Legendre invariant (LEINV). Although the LET has been known for more than 200 years, both the LEID and the LEINV are critical in modern optimization theory and methods. The purpose of this talk is to show the role the LEID and the LEINV play in both constrained and unconstrained optimization.