281. Warped proximal iterations for solving nonmonotone inclusions and applications
Invited abstract in session WC-6: Advances in monotone inclusions and related methods, stream Methods for non-/monotone inclusions and their applications.
Wednesday, 10:05 - 11:20Room: M:H
Authors (first author is the speaker)
| 1. | Dimitri Papadimitriou
|
| Belgium Research Center (Leuven, Belgium), MCO Institute & Université libre de Bruxelles (ULB) | |
| 2. | Cong Bang Vu
|
| 3NLab, Huawei Belgium Research Center (BeRC), Leuven, Belgium |
Abstract
In a real Hilbert space H, the monotone inclusion problem aims at finding a zero of a set-valued maximally monotone operator A. The term warped proximal iteration was recently introduced as generalization of the proximal point algorithm for finding a zero point of a maximally monotone operator A acting on H. Nevertheless, the maximal monotonicity of A restricts its applicability to the class of convex optimization problems as well as operator splitting methods for composite monotone inclusions. The solving of general nonmonotone inclusion, i.e., the inclusion where the operator A is nonmonotone, is an open and challenging research problem. For this purpose, the notion of r-(co)hypomonotonicity has been introduced to guarantee the convergence of the generated sequence. From this perspective, our first objective is to extend the
definition of r-hypomotonicity. The second is to investigate the weak convergence property of the warped proximal iteration as well as its various applications to (constrained) nonconvex optimization problems. In particular, we place our attention to the finding of KKT points for a class of nonconvex quadratic programming problems with equality constraints.
Keywords
- SS - Advances in Nonlinear Optimization and Applications
Status: accepted
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