An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917391988948992 |
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| author | Kouri, Drew P. |
| author_facet | Kouri, Drew P. |
| contents | We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the use of inexact value and derivative information, enabling the solution of infinite-dimensional problems governed by, e.g., partial differential equations (PDEs). We prove global convergence of our method and under additional regularity assumptions, demonstrate that the sequence of iterates accumulates at a stationary point of our target problem. We demonstrate our method's efficiency on two PDE-constrained optimization examples, showing that its performance is invariant to the PDE discretization size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07216 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming Kouri, Drew P. Optimization and Control 49M29, 49M37, 65K10, 90C15, 93E20 We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the use of inexact value and derivative information, enabling the solution of infinite-dimensional problems governed by, e.g., partial differential equations (PDEs). We prove global convergence of our method and under additional regularity assumptions, demonstrate that the sequence of iterates accumulates at a stationary point of our target problem. We demonstrate our method's efficiency on two PDE-constrained optimization examples, showing that its performance is invariant to the PDE discretization size. |
| title | An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming |
| topic | Optimization and Control 49M29, 49M37, 65K10, 90C15, 93E20 |
| url | https://arxiv.org/abs/2604.07216 |