Extreme Point Pursuit -- Part I: A Framework for Constant Modulus Optimization
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913574782238720 |
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| author | Liu, Junbin Liu, Ya Ma, Wing-Kin Shao, Mingjie So, Anthony Man-Cho |
| author_facet | Liu, Junbin Liu, Ya Ma, Wing-Kin Shao, Mingjie So, Anthony Man-Cho |
| contents | This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints, and several types of binary assignment constraints. Capitalizing on the basic principles of concave minimization and error bounds, we study a convex-constrained penalized formulation for general CM problems. The advantage of such formulation is that it allows us to leverage non-convex optimization techniques, such as the simple projected gradient method, to build algorithms. As the first part of this study, we explore the theory of this framework. We study conditions under which the formulation provides exact penalization results. We also examine computational aspects relating to the use of the projected gradient method for each type of CM constraint. Our study suggests that the proposed framework has a broad scope of applicability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extreme Point Pursuit -- Part I: A Framework for Constant Modulus Optimization Liu, Junbin Liu, Ya Ma, Wing-Kin Shao, Mingjie So, Anthony Man-Cho Signal Processing Optimization and Control This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints, and several types of binary assignment constraints. Capitalizing on the basic principles of concave minimization and error bounds, we study a convex-constrained penalized formulation for general CM problems. The advantage of such formulation is that it allows us to leverage non-convex optimization techniques, such as the simple projected gradient method, to build algorithms. As the first part of this study, we explore the theory of this framework. We study conditions under which the formulation provides exact penalization results. We also examine computational aspects relating to the use of the projected gradient method for each type of CM constraint. Our study suggests that the proposed framework has a broad scope of applicability. |
| title | Extreme Point Pursuit -- Part I: A Framework for Constant Modulus Optimization |
| topic | Signal Processing Optimization and Control |
| url | https://arxiv.org/abs/2403.06506 |