Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.18997 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913050796228608 |
|---|---|
| author | Li, Qifeng |
| author_facet | Li, Qifeng |
| contents | This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint violation, PECO also explicitly requires feasibility for all events whose probability exceeds a prescribed threshold. This guarantees that solutions remain valid across all high-probability realizations of uncertainty. To solve PECO, we proposed a data-embedded program (DEP) which directly incorporates historical measurements of the uncertain parameters to obtain a deterministic approximation for PECO. While existing solution methods for optimization problems under uncertainty rely heavily on convexity or linearity assumptions, the proposed data-embedded solution paradigm provides a unique opportunity for solving nonlinear and nonconvex PECOs. The effectiveness of this approach depends on properly estimating the number of elements in the family of solution-determining data sets. As we enter the era of big data, this information can be properly estimated by leveraging the power of machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Data-embedded Solution Paradigm for Nonconvex Probable Event Constrained Optimization Li, Qifeng Optimization and Control This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint violation, PECO also explicitly requires feasibility for all events whose probability exceeds a prescribed threshold. This guarantees that solutions remain valid across all high-probability realizations of uncertainty. To solve PECO, we proposed a data-embedded program (DEP) which directly incorporates historical measurements of the uncertain parameters to obtain a deterministic approximation for PECO. While existing solution methods for optimization problems under uncertainty rely heavily on convexity or linearity assumptions, the proposed data-embedded solution paradigm provides a unique opportunity for solving nonlinear and nonconvex PECOs. The effectiveness of this approach depends on properly estimating the number of elements in the family of solution-determining data sets. As we enter the era of big data, this information can be properly estimated by leveraging the power of machine learning. |
| title | A Data-embedded Solution Paradigm for Nonconvex Probable Event Constrained Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.18997 |