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学者姓名：林蓝玉
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Abstract ：
The generalized convex nearly isotonic regression problem addresses a least squares regression model that incorporates both sparsity and monotonicity constraints on the regression coefficients. In this paper, we introduce an efficient semismooth Newton-based augmented Lagrangian (Ssnal) algorithm to solve this problem. We demonstrate that, under reasonable assumptions, the Ssnal algorithm achieves global convergence and exhibits a linear convergence rate. Computationally, we derive the generalized Jacobian matrix associated with the proximal mapping of the generalized convex nearly isotonic regression regularizer and leverage the second-order sparsity when applying the semismooth Newton method to the subproblems in the Ssnal algorithm. Numerical experiments conducted on both synthetic and real datasets clearly demonstrate that our algorithm significantly outperforms first-order methods in terms of efficiency and robustness.
Keyword ：
augmented Lagrangian algorithm augmented Lagrangian algorithm generalized convex nearly isotonic regression generalized convex nearly isotonic regression semismooth Newton method semismooth Newton method
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| GB/T 7714 | Xu, Yanmei , Lin, Lanyu , Liu, Yong-Jin . A Semismooth Newton-Based Augmented Lagrangian Algorithm for the Generalized Convex Nearly Isotonic Regression Problem [J]. | MATHEMATICS , 2025 , 13 (3) . |
| MLA | Xu, Yanmei 等. "A Semismooth Newton-Based Augmented Lagrangian Algorithm for the Generalized Convex Nearly Isotonic Regression Problem" . | MATHEMATICS 13 . 3 (2025) . |
| APA | Xu, Yanmei , Lin, Lanyu , Liu, Yong-Jin . A Semismooth Newton-Based Augmented Lagrangian Algorithm for the Generalized Convex Nearly Isotonic Regression Problem . | MATHEMATICS , 2025 , 13 (3) . |
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Abstract ：
The Fantope-constrained sparse principal subspace estimation problem is initially proposed Vu et al. (Vu et al., 2013). This paper investigates a semismooth Newton based proximal point (P PASSN ) algorithm for solving the equivalent form of this problem, where a semismooth Newton (S SN ) method is utilized to optimize the inner problems involved in the P PASSN algorithm. Under standard conditions, the P PASSN algorithm is proven to achieve global convergence and asymptotic superlinear convergence rate. Computationally, we derive nontrivial expressions the Fantope projection and its generalized Jacobian, which are key ingredients for the P PASSN algorithm. Some numerical results on synthetic and real data sets are presented to illustrate the effectiveness of the proposed P PASSN algorithm for large-scale problems and superiority over the alternating direction method of multipliers (ADMM).
Keyword ：
Fantope projection Fantope projection Generalized Jacobian Generalized Jacobian Proximal point algorithm Proximal point algorithm Semismooth Newton algorithm Semismooth Newton algorithm
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| GB/T 7714 | Liu, Yong-Jin , Wan, Yuqi , Lin, Lanyu . An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2024 , 475 . |
| MLA | Liu, Yong-Jin 等. "An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem" . | APPLIED MATHEMATICS AND COMPUTATION 475 (2024) . |
| APA | Liu, Yong-Jin , Wan, Yuqi , Lin, Lanyu . An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem . | APPLIED MATHEMATICS AND COMPUTATION , 2024 , 475 . |
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