Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2026
|
| Online Access: | https://doi.org/10.5281/zenodo.18830170 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- <p><span>This paper proposes a novel convex optimization theoretical framework—Risk-Embedded Conic Programming (RECP). This theory breaks through the traditional modeling paradigm of "risk entering the objective function" by endogenizing the risk envelope set Q into a dual cone-generating substructure, thereby geometrically reshaping the original feasible region. Specifically, we construct a risk-generating cone R_Q and a risk-embedding cone K_Q, so that the risk metric no longer serves as a correction term for the objective function but becomes the structural generation mechanism of the cone. This paper proves that under the general Banach space framework, the risk-embedding cone maintains closed convexity, self-dual stability, and polar-ray structural stability; under the Slater condition, RECP maintains strong duality and zero dual gap; and this model is equivalent to a single closed convex cone programming in an extended space. Furthermore, we establish the risk-geometric mapping theorem, the risk polar-ray decomposition theorem, and the risk steady-state extremum existence theorem. Theoretically, this framework rigorously includes robust optimization, partially robust optimization, and consistent risk metric models as special cases, thus constituting a structural extension of cone programming theory. The concept of risk geometric embedding proposed in this paper provides a unified mathematical foundation for high-dimensional uncertain optimization</span>.</p>