Howard Heaton – Optimization Online

Asynchronous Sequential Inertial Iterations for Common Fixed Points Problems with an Application to Linear Systems

Published: 2018/08/15, Updated: 2019/01/24

Constrained Nonlinear Optimization, Convex Optimization asynchronous sequential iterations, convex feasibility problem, drop algorithm, fixed-point iteration, kaczmarz method, nonexpansive operator

The common fixed points problem requires finding a point in the intersection of fixed points sets of a finite collection of operators. Quickly solving problems of this sort is of great practical importance for engineering and scientific tasks (e.g., for computed tomography). Iterative methods for solving these problems often employ a Krasnosel’skii-Mann type iteration. We … Read more

Derivative-Free Superiorization With Component-Wise Perturbations

Published: 2018/03/30

Yair Censor

Howard Heaton

Reinhard W. Schulte

Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization component-wise perturbations, derivative-free, feasibility-seeking, image reconstruction, perturbation resilience, superiorization

Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints-compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbations resilience, and proactively perturbing its iterates accordingly to steer them toward a feasible point with reduced value of the target function. When the perturbation steps are computationally efficient, this … Read more