HIGHLIGHTS
SUMMARY
The Lagrangian multipliers ("dual" variables) are the decision variables with respect to the dual problem, and it is assumed that the set of optimal solutions is not empty. The multipliers are subsequently projected onto the positive orthant delineated by restrictions ≥ 0. To overcome the first two of the difficulties above, the Surrogate Subgradient method was developed by23 whereby the exact optimality of the relaxed problem (or even subproblems) is not required. Unlike that in Polyak`s formula, parameter γ is less than 1 to guarantee that q( * ) > L(x̃ k, ỹ k, k ) so that . . .
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