In this note we give a new, simple proof of the standard first and second order necessary conditions, under the Mangasarian-Fromovitz constraint qualification (MFCQ), for non-linear programming problems. We work under a mild constraint qualification, which is implied by MFCQ. This makes it...

The origin of the second best article is described and criticisms assessed. Distortions making impossible the achievement of either first or second best optima are outlined. Attempts to establish the applicability of first best rules are criticised, as are general rules for making piecemeal...

A a set-valued optimization problem min<Subscript> C </Subscript> F(x), x ∈X <Subscript>0</Subscript>, is considered, where X <Subscript>0</Subscript> ⊂ X, X and Y are normed spaces, F: X <Subscript>0</Subscript> ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x <Superscript>0</Superscript>,y <Superscript>0</Superscript>), y <Superscript>0</Superscript> ∈F(x <Superscript>0</Superscript>), and are called...</superscript></superscript></superscript></superscript></subscript></subscript></subscript></subscript>

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a...

A a set-valued optimization problem min C F(x), x ∈X 0 , is considered, where X 0 ⊂ X, X and Y are normed spaces, F: X 0 ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x 0 ,y 0 ), y 0 ∈F(x 0 ), and are called...