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On the convexification procedure for nonconvex and nonsmooth infinite dimensional optimization problems. (English) Zbl 0755.49013
The paper gives a generalization and modification of a convexification procedure of D. P. Bertsekas [J. Optimization Theory Appl. 29, 169- 197 (1979; Zbl 0389.90080)] for infinite dimensional, nonsmooth and nonconvex optimization problems. A nonconvex minimization problem is being transformed into a convex parametrical minimization problem and an additional minimization of an everywhere Fréchet differentiable nonconvex function. The convexification of the nonconvex cost function $f$ to ensue by means of a strongly convex function $g$, so that $f+g$ is also a strongly convex function. One can prove a connection with the duality theory of J. F. Toland [J. Math. Anal. Appl. 66, 399-415 (1978; Zbl 0403.90066)] and give a descent method for the original problem.
Reviewer: H.Dietrich
##### MSC:
 49N15 Duality theory (optimization) 90C48 Programming in abstract spaces 49M05 Numerical methods in calculus of variations based on necessary conditions 90C26 Nonconvex programming, global optimization