Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
A parallel subgradient projections method for the convex feasibility problem
Journal of Computational and Applied Mathematics
Journal of Optimization Theory and Applications
Parallel application of block-iterative methods in medical imaging and radiation therapy
Mathematical Programming: Series A and B
Fractional programming by lower subdifferentiability techniques
Journal of Optimization Theory and Applications
Lower subdifferentiability of quadratic functions
Mathematical Programming: Series A and B
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Block-Iterative Algorithms with Underrelaxed Bregman Projections
SIAM Journal on Optimization
The Constraint Consensus Method for Finding Approximately Feasible Points in Nonlinear Programs
INFORMS Journal on Computing
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We study the behavior of subgradient projections algorithms for the quasiconvex feasibility problem of finding a point x* ∈ Rn that satisfies the inequalities f1(x*)≤0, f2(x*)≤0,..., fm(x*)≤0, where all functions are continuous and quasiconvex. We consider the consistent case when the solution set is nonempty. Since the Fenchel-Moreau subdifferential might be empty we look at different notions of the subdifferential and determine their suitability for our problem. We also determine conditions on the functions, that are needed for convergence of our algorithms. The quasiconvex functions on the left-hand side of the inequalities need not be differentiable but have to satisfy a Lipschitz or a Hölder condition.