Convergence Analysis of Algorithms for DC Programming

Thời gian: 14:00 đến 17:00 Ngày 07/11/2016

Địa điểm:

Báo cáo viên: Bùi Văn Định

Tóm tắt:

We consider the minimization problems of the form $P(\varphi, g, h)$: $\min\{f(x) = \varphi(x) + g(x) - h(x): x \in \mathcal{R}^n \}$, where $\varphi$ is a differentiable function, $g$ and $h$ are convex functions, and introduce iterative methods to finding a critical point of $f$ when $f$ is differentiable. We show that the point computed by proximal point algorithm at each iteration can be used to determine a descent direction for the objective function at this point. This algorithm can be considered as a combination of proximal point algorithm together with a linesearch step that uses this descent direction. We also study convergence results of these algorithms and the inertial proximal methods proposed by P.E. Maingé and A. Moudafi (SIAM J. Optim. 19(2008), 397-413.) under the main assumption that the objective function satisfies the Kurdika-Lojasiewicz property.