Abstract
For nonconvex problems, the saddle point equivalence of the Lagrangian approach need not hold. The nonexistence of a saddle point causes the generation of a dual gap at the solution point, and the Lagrangian approach then fails to give the solution to the original problem. Unfortunately, dual gaps are a fairly common phenomenon for engineering system design problems.
Methods which are available to resolve the dual gaps destroy the separability of separable systems. The present work employs the method of multipliers by Hestenes to resolve the dual gaps of engineering system design problems; it then develops an algorithmic procedure which preserves the separability characteristics of the system. The theoretical foundations of the proposed algorithm are developed, and examples are provided to clarify the approach taken.
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Communicated by R. Jackson
This work was supported by NSF Grant No. GK-18633.
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Stephanopoulos, G., Westerberg, A.W. The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization. J Optim Theory Appl 15, 285–309 (1975). https://doi.org/10.1007/BF00933339
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DOI: https://doi.org/10.1007/BF00933339