computerized tomography – Optimization Online

Projected subgradient minimization versus superiorization

Published: 2013/08/18

Biomedical Applications, Constrained Nonlinear Optimization bounded convergence, computerized tomography, constrained minimization, feasibility-seeking, image reconstruction, projected subgradient method, proximity function, strong perturbation resilience, superiorization

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region is “simple … Read more

Sequential Subspace Optimization Method for Large-Scale Unconstrained Problems

Published: 2005/10/26, Updated: 2005/10/30

Guy Narkiss

Michael Zibulevsky

Nonlinear Optimization, Unconstrained Optimization basis pursuit, computerized tomography, conjugate gradient method, large-scale optimization, subspace optimization

We present the Sequential Subspace Optimization (SESOP) method for large scale smooth unconstrained problems. At each iteration we search for a minimum of the objective function over a subspace spanned by the current gradient and by directions of few previous steps. We also include into this subspace the direction from the starting point to the … Read more