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Cooper and K. Kortanek, On representations of semi-infinite programs which have no duality gaps. Clarke, A new approach to Lagrange multipliers. Craven, Mathematical Programming and Control Theory.

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Chapman and Hall, London Dinh, V. Jeyakumar and G. Lee, Sequential Lagrangian conditions for convex programs with applications to semidefinite programming.

Theory Appl. Dinh, M. Goberna and M.


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Fajardo and M. Wiley, Chichester Gwinner, On results of Farkas type. Hiriart Urruty and C. Springer-Verlag, Berlin Jeyakumar, Asymptotic dual conditions characterizing optimality for infinite convex programs.

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Floudas and P. Pardalos Eds. Jeyakumar, Characterizing set containments involving infinite convex constraints and reverse-convex constraints. Jeyakumar, A. Rubinov, B. Glover and Y. Ishizuka, Inequality systems and global optimization. Jeyakumar, G. Lee and N. Dinh, New sequential Lagrange multiplier conditions characterizing optimality without constraint qualifications for convex programs. Jeyakumar, N. Dinh and G. Unpublished manuscript. Laurent, Approximation et optimization. Hermann, Paris Li and K. Ng, On constraint qualification for an infinite system of convex inequalities in a Banach space.

Instead of first outlining everything relevant about conjugate convex functions and then deriving its consequences for optimization, I have tried to introduce areas of basic theory only as they became needed and their significance for the study of dual problems more apparent. In particular, general results on the calculation of conjugate functions have been postponed nearly to the end. I have also attempted to show just where it is that convexity is needed, and what remains true if certain convexity or lower-semicontinuity assumptions are dropped.

Some Limit Theorems in Statistics

The notation and terminology of [13] have been changed somewhat to make an easier introduction to the subject. The duality theorem for linear programming problems, for instance, turns out to be an analogue of an algebraic identity relating a linear transformation and its adjoint. For more on this point of view and its possible fertility for applications such as to mathematical economics, see [24]. Sign in Help View Cart.

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Fenchel Conjugates - Part 2