An MM Algorithm for Split Feasibility Problems
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Publication:150985
DOI10.48550/ARXIV.1612.05614zbMATH Open1416.90048arXiv1612.05614OpenAlexW2885174950WikidataQ129479545 ScholiaQ129479545MaRDI QIDQ150985
Jason Xu, Kenneth Lange, Meng Yang, Eric C. Chi, Kenneth Lange, Meng Yang, Jason Xu, Eric C. Chi
Publication date: 16 December 2016
Published in: Computational Optimization and Applications (Search for Journal in Brave)
Abstract: The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including convex feasibility, linear complementarity, and regression with constraint sets. When a feasible point does not exist, solution methods that proceed by minimizing a proximity function can be used to obtain optimal approximate solutions to the problem. We present an extension of the proximity function approach that generalizes the linear split feasibility problem to allow for non-linear mappings. Our algorithm is based on the principle of majorization-minimization, is amenable to quasi-Newton acceleration, and comes complete with convergence guarantees under mild assumptions. Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences. We explore several examples illustrating the merits of non-linear formulations over the linear case, with a focus on optimization for intensity-modulated radiation therapy.
Full work available at URL: https://arxiv.org/abs/1612.05614
intensity modulated radiation therapyconstrained regressionmajorize-minimizenonlinear split feasibilityproximity function minimization
Cites Work
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Penalized likelihood regression for generalized linear models with non-quadratic penalties
- Distance majorization and its applications
- Applications of variational analysis to a generalized Fermat-Torricelli problem
- A note on the split common fixed-point problem for quasi-nonexpansive operators
- Cyclic algorithms for split feasibility problems in Hilbert spaces
- Algorithms for the split variational inequality problem
- A quasi-Newton acceleration for high-dimensional optimization algorithms
- A generalized projection-based scheme for solving convex constrained optimization problems
- Perturbed projections and subgradient projections for the multiple-sets split feasibility problem
- A multiprojection algorithm using Bregman projections in a product space
- Proximal algorithms in statistics and machine learning
- Alternating minimization as sequential unconstrained minimization: a survey
- General method for solving the split common fixed point problem
- Linear and nonlinear programming
- Hard-constrained inconsistent signal feasibility problems
- Weak and strong superiorization: between feasibility-seeking and minimization
- MM Optimization Algorithms
- The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations
- Solving a Generalized Heron Problem by Means of Convex Analysis
- Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces
- Algorithms for Nonnegative Matrix Factorization with the β-Divergence
- Applications of variational analysis to a generalized Heron problem
- The multiple-sets split feasibility problem and its applications for inverse problems
- A Selective Overview of Variable Selection in High Dimensional Feature Space (Invited Review Article)
- A variable Krasnosel'skii–Mann algorithm and the multiple-set split feasibility problem
- Numerical Analysis for Statisticians
- Row-Action Methods for Huge and Sparse Systems and Their Applications
- Variational Analysis
- Iterative oblique projection onto convex sets and the split feasibility problem
- ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES
- Sparse Reconstruction by Separable Approximation
- Solving monotone inclusions via compositions of nonexpansive averaged operators
- Optimizing the Delivery of Radiation Therapy to Cancer Patients
- Iterative projection onto convex sets using multiple Bregman distances
- L 1-Regularization Path Algorithm for Generalized Linear Models
- A self-adaptive projection-type method for nonlinear multiple-sets split feasibility problem
- Regularization and Variable Selection Via the Elastic Net
- A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization
- Sequential unconstrained minimization algorithms for constrained optimization
- Signal Recovery by Proximal Forward-Backward Splitting
- Optimization
- Mathematical optimization in intensity modulated radiation therapy
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Uses Software
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