183 research outputs found
Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces
We model a problem motivated by road design as a feasibility problem.
Projections onto the constraint sets are obtained, and projection methods for
solving the feasibility problem are studied. We present results of numerical
experiments which demonstrate the efficacy of projection methods even for
challenging nonconvex problems
String-Averaging Projected Subgradient Methods for Constrained Minimization
We consider constrained minimization problems and propose to replace the
projection onto the entire feasible region, required in the Projected
Subgradient Method (PSM), by projections onto the individual sets whose
intersection forms the entire feasible region. Specifically, we propose to
perform such projections onto the individual sets in an algorithmic regime of a
feasibility-seeking iterative projection method. For this purpose we use the
recently developed family of Dynamic String-Averaging Projection (DSAP) methods
wherein iteration-index-dependent variable strings and variable weights are
permitted. This gives rise to an algorithmic scheme that generalizes, from the
algorithmic structural point of view, earlier work of Helou Neto and De Pierro,
of Nedi\'c, of Nurminski, and of Ram et al.Comment: Optimization Methods and Software, accepted for publicatio
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