Projection Methods and Constraint Shape

Invited abstract in session MB-54: Projection methods in optimization problems 2, stream Convex Optimization.

Area: Continuous Optimization

Monday, 10:30-12:00
Room: Building PA, Room B

Authors (first author is the speaker)

1. John Chinneck
Systems and Computer Engineering, Carleton University

Abstract

Projection methods are commonly applied to sets of constraints defining a convex feasible region where their favorable properties are well understood. Under the name of "constraint consensus methods" they are also applied as heuristics when the convexity properties of the feasible region are unknown, which is frequently the case in practice. Suppose that the "shape" (linear, convex, concave, both) of each nonlinear constraint could be discovered (and hence the convexity properties of the feasible region could be deduced). Could this information be used to accelerate projection methods seeking a feasible point for the set of constraints? We develop methods for estimating the shape of nonlinear functions as the constraint consensus solution proceeds and show how to use this information to increase speed by adjusting the algorithms as they run, primarily by inserting linear or quadratic correction steps to the updates.

Keywords

Status: accepted


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