Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets

By Songnian He, Caiping Yang. 2013

149 citations recorded by the source corpus.

Consider the variational inequality of finding a point satisfying the property , for all , where is the intersection of finite level sets of convex functions defined on a real Hilbert space and is an -Lipschitzian and -strongly monotone operator. Relaxed and self-adaptive iterative algorithms are devised for computing the unique solution of . Since our algorithm avoids calculating the projection (calculating by computing several sequences of projections onto half-spaces containing the original domain ) directly and has no need to know any information of the constants and , the implementation of our algorithm is very easy. To prove strong convergence of our algorithms, a new lemma is established, which can be used as a fundamental tool for solving some nonlinear problems.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/88cc2f802ad77b1c7b0c0ea8b65b4988595865f5

Citations in the corpus

• Common zero point for a finite family of inclusion problems of accretive mappings in Banach spaces (2018, unknown): “4 [20]: Let {sn} be a sequence of nonnegative real numbers such that sn+1 ≤ (1 − γn)sn + γnτn”
• An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces (2018, unknown): “[26] Assume {sn} is a sequence of nonnegative real numbers such that sn+1 ≤ (1 − δn)sn + δnτn, n ≥ 1 (2.”