The calculus of variations is a method for finding stable solutions to optimization problems. To find unstable ones, Morse theory and min-max methods are more appropriate, despite difficulties in applying them universally. Professor Ghoussoub describes a new point of view that may help when dealing with such difficulties. Building upon min-max approach, he systematically develops a general theory and presents a whole new array of duality and perturbation methods. The the book reasonably self-contained. Consequently, it should be accessible to all mathematicians,economists and engineers working in nonlinear analysis or optimization.

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