Polyhedral-Conic Duality for Exact Mixed-Integer Nonconvex Optimization
Fuente:
Zenodo
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Recurso digital |
| Pubblicazione: |
Zenodo
2025
|
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866901537721155584 |
|---|---|
| author | Revista, Zen MATH, 10 |
| author_facet | Revista, Zen MATH, 10 |
| contents | This paper introduces a novel theoretical framework for solving exact mixed-integer nonconvex optimization problems based on polyhedral-conic duality. Mixed-integer nonconvex programs are pervasive across science and engineering, yet their exact solution remains a significant challenge due to the combinatorial nature of integer variables and the difficulties posed by nonconvexity. Traditional approaches often rely on relaxations, branch-and-bound schemes, or heuristics, which may not guarantee global optimality. We propose a systematic development of a dual problem that leverages the interplay between polyhedral representations of integer feasible regions and conic representations of nonconvex functions. By carefully constructing a dual problem, we aim to derive tight lower bounds and, under certain conditions, achieve exact solutions through strong duality. This approach provides a new lens through which to analyze and develop algorithms for these challenging problem classes, offering potential avenues for improved computational performance and broader applicability. We discuss the theoretical properties of this duality, its relationship to existing duality theories, and its implications for algorithm design and solution quality. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17804564 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Polyhedral-Conic Duality for Exact Mixed-Integer Nonconvex Optimization Revista, Zen MATH, 10 This paper introduces a novel theoretical framework for solving exact mixed-integer nonconvex optimization problems based on polyhedral-conic duality. Mixed-integer nonconvex programs are pervasive across science and engineering, yet their exact solution remains a significant challenge due to the combinatorial nature of integer variables and the difficulties posed by nonconvexity. Traditional approaches often rely on relaxations, branch-and-bound schemes, or heuristics, which may not guarantee global optimality. We propose a systematic development of a dual problem that leverages the interplay between polyhedral representations of integer feasible regions and conic representations of nonconvex functions. By carefully constructing a dual problem, we aim to derive tight lower bounds and, under certain conditions, achieve exact solutions through strong duality. This approach provides a new lens through which to analyze and develop algorithms for these challenging problem classes, offering potential avenues for improved computational performance and broader applicability. We discuss the theoretical properties of this duality, its relationship to existing duality theories, and its implications for algorithm design and solution quality. |
| title | Polyhedral-Conic Duality for Exact Mixed-Integer Nonconvex Optimization |
| url | https://doi.org/10.5281/zenodo.17804564 |