ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 49, 90 Antipin, Anatoly, Computing Center of Russ. Acad. of Sciences, Russia: To Solving of Equilibrium Programming Problems This talk will deal with the problem to compute a fixed point v^{∗} ∈ Ω^{∗} of the extreme constrained map

v^{∗} ∈ Argmin{Φ(v^{∗}, w) | g(w) ≤ 0, w ∈ Ω},  (1)

where Φ : R^{n} ×R^{n} → R, Ω ⊆ R^{n} is a convex closed set, Φ(v, w) is a convex function in w ∈ Ω for every v ∈ Ω, Ω^{∗} ⊆ Ω. It is supposed that the extreme map is defined for all v ∈ Ω and the solution set Ω^{∗} of (1) is nonempty. Problem (1) contains as a special cases of noncooperative games with Nash equilibria, inverse optimization problems, economic equilibrium problems and others. To solve problem (1) it is offered a splitting-approach such that considered problem can be reduced to solving jointly of convex and saddle programming problems.