Limit modifications in optimization and their applications to saddle point problems (Q579146)

A multiplicative type of modification in the optimization problem inf\(\{\) f(x): \(x\in A\}\) with a sequence of functions \(\{H_ n(x)\}_{n\in N}\) is discussed in the present work to yield the problem \(\inf \{f(x)H_ n(H):\) \(x\in A\}\). We discuss the convergence properties for this class of modifications. The results obtained are applied to modify saddle point problems with partial modifications. It turns out that the present modification is yet another type of modification differing from the types already discussed by \textit{I. Behar} [SIAM J. Control Optimization 17, 673-688 (1979; Zbl 0437.90100)]. We apply our results for convex-concave saddle point problems as well with total modification.