The data-compatibility approach to constrained optimization, proposed here, strives to a point that is “close enough” to the solution set and whose target function value is “close enough” to the constrained minimum value. These notions can replace analysis of asymptotic convergence to a solution point of infinite sequences generated by specific algorithms. We consider a problem of minimizing a convex function over the intersection of the fixed point sets of nonexpansive mappings and demostrate the data-compatibility of the Hybrid Subgradient Method (HSM). A string-averaging HSM is obtained as a by-product and relevance to the minimization over disjoint hard and soft constraints sets is discussed.
Bibliographical noteFunding Information:
We greatly appreciate the comprehensive and very constructive referee report that helped us improve the paper. The work of Y.C. is supported by the ISF-NSFC joint research program grant No. 2874/19.
© 2021 Journal of Applied and Numerical Optimization.
- Constrained minimization
- Hybrid subgradient method
- Proximity function
ASJC Scopus subject areas
- Computational Mathematics
- Control and Optimization
- Modeling and Simulation
- Numerical Analysis