The Gradient Projection Method with Exact Line Search

Authors:
William W. Hager;Soonchul Park
Affiliations:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA (e-mail: hager@math.ufl.edu);Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA (e-mail: scp@math.ufl.edu.)
Venue:
Journal of Global Optimization
Year:
2004

Citing 4
Cited 0

Projected gradient methods for linearly constrained problems

Mathematical Programming: Series A and B
On the convergence of projected gradient processes to singular critical points

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An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds

Mathematical Programming: Series A and B
Graph Partitioning and Continuous Quadratic Programming

SIAM Journal on Discrete Mathematics

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Abstract

The gradient projection algorithm for function minimization is often implemented using an approximate local minimization along the projected negative gradient. On the other hand, for some difficult combinational optimization problems, where a starting guess may be far from a solution, it may be advantageous to perform a nonlocal (exact) line search. In this paper we show how to evaluate the piece-wise smooth projection associated with a constraint set described by bounds on the variables and a single linear equation. When the NP hard graph partitioning problem is formulated as a continuous quadratic programming problem, the constraints have this structure.