Convergence of Toland's critical points for sequences of D.C. functions and application to the resolution of semilinear elliptic problems

• Autorzy: Yassine A. , Alaa N. , Elhilali Alaoui A.
• Języki publikacji: EN

Abstrakty

EN

We prove that if a sequence (fn)n of D.C. functions (Difference of two Convex functions) converges to a D.C. function f in some appropriate way and if un is a critical point of fn, in the sense described by Toland, and is such that (un)n converges to u, then a is a critical point of f, still in Toland's sense. We also build a new algorithm which searches for this critical point u and then apply it in order to compute the solution of a semilinear elliptic equation.

Słowa kluczowe

EN

dc functions; non-convex optimization; normalized D.C. decomposition; proximal algorithm; semilinear elliptic problem; Toland's critical point

PL

algorytm proksymalny; funkcje D.C.; optymalizacja niewypukła; punkt krytyczny Tolanda; semiliniowe zagadnienie eliptyczne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2001
• Tom: Vol. 30, no 4
• Strony: 405--417
• Opis fizyczny: Bibliogr. 25 poz.,

Twórcy

autor

Yassine A.

autor

Alaa N.

autor

Elhilali Alaoui A.