Proof of Strong Duality

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Description

This lecture covers the proof of strong duality in optimization problems, demonstrating the relationship between primal and dual problems, the existence of valid Lagrange multipliers, and the convexity of the objective function. Examples of Rayleigh quotient optimization are provided to illustrate the concepts discussed.

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https://mediaspace.epfl.ch/media/0_5r3nw1xy

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In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.

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