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Active-set Newton methods and partial smoothness

Adrian Lewis(adrian.lewis***at***cornell.edu)
Calvin Wylie(cjw278***at***cornell.edu)

Abstract: Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active-set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

Keywords: partial smoothness, active set identification, variational inequality

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Complementarity and Variational Inequalities

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: School of ORIE, Cornell University

Download: [PDF]

Entry Submitted: 02/02/2019
Entry Accepted: 02/02/2019
Entry Last Modified: 02/02/2019

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