For a given solution to a semidefinite programming problem, it is easy to check its feasibility and to calculate the amount of constraint violation. But how do you check optimality or near optimality in terms of the objective value? Duality theory provides an answer to these questions. The idea is to associate the semidefinite program with a dual semidefinite program in such a way that upper and lower bounds on the optimal value can be calculated, once feasible solutions to the SDP problem and its dual are known.
KeywordsStrong Duality Real Linear Space Improve Direction Strong Duality Theorem Dual Characterization
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