Abstract
The augmented penalty function is used to solve optimization problems with constraints and for faster convergence while adopting gradient techniques. In this note, an attempt is made to show that, ifx* ∈S maximizes the function
thenx* maximizesf(x) over all thosex ∈S such that
under the assumptions that the λ j 's andk are nonnegative, real numbers. Here,W(x, λ,K),f(x), andC j (x),j=1, 2,...,n, are real-valued functions andC j (x) ≥ 0 forj=1, 2,...,n and for allx. The above result is generalized considering a more general form of the augmented penalty function.
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Communicated by M. R. Hestenes
The authors thank the reviewer for timely suggestions.
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Raghavendra, V., Rao, K.S.P. A note on optimization using the augmented penalty function. J Optim Theory Appl 12, 320–324 (1973). https://doi.org/10.1007/BF00935111
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DOI: https://doi.org/10.1007/BF00935111