2018 Joint Seminar and Research Camp (JSRC) program on Mathematical Science

P000009

Rapid gradient penalty schemes and convergence for solving constrained convex optimization problems in Hilbert spaces

*Natthaphon Artsawang (Department of mathematics, faculty of science, Naresuan University, Phitsanulok)
Kasamsuk Ungchittrakool (Department of mathematics, faculty of science, Naresuan University, Phitsanulok)

The purposes of this paper are to establish and study the convergence of a new gradient scheme with penalization terms called rapid gradient penalty algorithm (${\bf RGPA}$) for minimzing a convex differentiable function over the set of minimizers of convex, lower semi continuous and differentiable constrained function. Under the observation of some appropriate choices for the available properties of the considered functions and scalars, we can generate the suitable algorithm that weakly converges to a minimal solution of the considered constraint minimization problem. Further, we also provide a numerical example to compare between the rapid gradient penalty algorithm (${\bf RGPA}$) and the (${\bf DGS}$) algorithm introduced by Peypouquet [7].
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