Chance-Constrained Optimization with Complex Variables
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915226610302976 |
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| author | Madani, Raneem Lisser, Abdel |
| author_facet | Madani, Raneem Lisser, Abdel |
| contents | Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in stochastic optimization involving complex random variables, termed the Complex Chance-Constrained Problem (CCCP). The study specifically examines the linear CCCP under complex normal distributions for two scenarios: one with individual probabilistic constraints and the other with joint probabilistic constraints. For the individual case, the core methodology reformulates the CCCP into a deterministic Second-Order Cone Programming (SOCP) problem, ensuring equivalence to the original CCCP. For the joint case, an approximation is achieved by deriving suitable upper and lower bounds, which also leads to a SOCP formulation. Finally, numerical experiments on a signal processing application, specifically the Minimum Variance Beamforming problem with mismatch using MVDR, demonstrate that the proposed formalism outperforms existing approaches in the literature. A comparative analysis between the joint and individual CCCP cases is also included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chance-Constrained Optimization with Complex Variables Madani, Raneem Lisser, Abdel Optimization and Control Probability Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in stochastic optimization involving complex random variables, termed the Complex Chance-Constrained Problem (CCCP). The study specifically examines the linear CCCP under complex normal distributions for two scenarios: one with individual probabilistic constraints and the other with joint probabilistic constraints. For the individual case, the core methodology reformulates the CCCP into a deterministic Second-Order Cone Programming (SOCP) problem, ensuring equivalence to the original CCCP. For the joint case, an approximation is achieved by deriving suitable upper and lower bounds, which also leads to a SOCP formulation. Finally, numerical experiments on a signal processing application, specifically the Minimum Variance Beamforming problem with mismatch using MVDR, demonstrate that the proposed formalism outperforms existing approaches in the literature. A comparative analysis between the joint and individual CCCP cases is also included. |
| title | Chance-Constrained Optimization with Complex Variables |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2504.03028 |