Journal article
Complexity of an inexact proximal-point penalty method for constrained smooth non-convex optimization
Computational optimization and applications, Vol.82(1), pp.175-224
05/01/2022
DOI: 10.1007/s10589-022-00358-y
Abstract
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. This method approximately solves a sequence of subproblems, each of which is formed by adding to the original objective function a proximal term and quadratic penalty terms associated to the constraint functions. Under a weak-convexity assumption, each subproblem is made strongly convex and can be solved effectively to a required accuracy by an optimal gradient-based method. The computational complexity of this approach is analyzed separately for the cases of convex constraint and non-convex constraint. For both cases, the complexity results are established in terms of the number of proximal gradient steps needed to find an epsilon-stationary point. When the constraint functions are convex, we show a complexity result of <(O)overtilde>(epsilon(-5/2)) to produce an epsilon-stationary point under the Slater's condition. When the constraint functions are non-convex, the complexity becomes (O) over tilde(epsilon(-3)) if a non-singularity condition holds on constraints and otherwise (O) over tilde(epsilon(-4)) if a feasible initial solution is available.
Details
- Title: Subtitle
- Complexity of an inexact proximal-point penalty method for constrained smooth non-convex optimization
- Creators
- Qihang Lin - University of IowaRunchao Ma - University of IowaYangyang Xu - Rensselaer Polytechnic Institute
- Resource Type
- Journal article
- Publication Details
- Computational optimization and applications, Vol.82(1), pp.175-224
- Publisher
- Springer Nature
- DOI
- 10.1007/s10589-022-00358-y
- ISSN
- 0926-6003
- eISSN
- 1573-2894
- Number of pages
- 50
- Grant note
- DMS-2053493 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 05/01/2022
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380486102771
Metrics
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