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学者姓名：王博
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Abstract ：
讨论一般随机二阶锥互补约束问题的求解算法.为处理模型中的不确定性,算法采用样本平均近似(SAA)抽样技术.不同于之前的工作,设计了一般光滑化SAA算法框架,可以在满足要求的一类光滑化函数中根据需要进行选择,从而构造光滑化SAA算法,并保证收敛性.具体的,若SOCMPCC线性无关约束规范等条件成立,则算法构造子问题的稳定点和最优解分别以概率1收敛到原问题的C稳定点和最优解.最后具体给出两个光滑化函数与其对应光滑化SAA算法的例子,由一般光滑化算法框架可得这两种算法收敛.
Keyword ：
二阶锥 二阶锥 互补约束优化 互补约束优化 样本平均近似(SAA) 样本平均近似(SAA) 随机优化 随机优化
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| GB/T 7714 | 王博 , 初丽 . 随机二阶锥互补约束优化模型的一般光滑化SAA方法 [J]. | 福州大学学报（自然科学版） , 2023 , 51 (1) : 13-19 . |
| MLA | 王博 等. "随机二阶锥互补约束优化模型的一般光滑化SAA方法" . | 福州大学学报（自然科学版） 51 . 1 (2023) : 13-19 . |
| APA | 王博 , 初丽 . 随机二阶锥互补约束优化模型的一般光滑化SAA方法 . | 福州大学学报（自然科学版） , 2023 , 51 (1) , 13-19 . |
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Abstract ：
本文讨论一类随机的二阶锥二次规划逆问题,该模型是一个含有二阶锥互补约束的随机二次规划模型,对解释部分实际问题有着一定的优势。为了求解该模型,本文引入了随机抽样技术和互补约束光滑化近似技术,得到问题的近似子问题。本文证明,只要子问题的解是存在且收敛的,则该极限以概率一是原问题的C-稳定点;若严格互补条件和二阶必要性条件成立,则该极限以概率1是原问题的M-稳定点。一个简单的数值实验验证了该算法具有一定的可行性。
Keyword ：
二阶锥优化 二阶锥优化 互补约束 互补约束 随机抽样 随机抽样
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| GB/T 7714 | 王博 , 初丽 , 张立卫 et al. 随机二阶锥二次规划逆问题的SAA方法 [J]. | 运筹学学报 , 2022 , (02) : 31-44 . |
| MLA | 王博 et al. "随机二阶锥二次规划逆问题的SAA方法" . | 运筹学学报 02 (2022) : 31-44 . |
| APA | 王博 , 初丽 , 张立卫 , 张宏伟 . 随机二阶锥二次规划逆问题的SAA方法 . | 运筹学学报 , 2022 , (02) , 31-44 . |
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A stochastic mathematical program model with second-order cone complementarity constraints (SSOCMPCC) is introduced in this paper. It can be considered as a non-trivial extension of stochastic mathematical program with complementarity constraints, and could arise from a hard-to-handle class of bilivel second-order cone programming and inverse stochastic second-order cone programming. By introducing the Chen-Harker-Kanzow-Smale (CHKS) type function to replace the projection operator onto the second-order cone, a smoothing sample average approximation (SAA) method is proposed for solving the SSOCMPCC problem. It can be shown that with proper assumptions, as the sample size goes to infinity, any cluster point of global solutions of the smoothing SAA problem is a global solution of SSOCMPCC almost surely, and any cluster point of stationary points of the former problem is a C-stationary point of the latter problem almost surely. C-stationarity can be strengthened to M-stationarity with additional assumptions. Finally, we report a simple illustrative numerical test to demonstrate our theoretical results.
Keyword ：
complementarity constraints complementarity constraints second-order cone second-order cone Stochastic mathematical programming Stochastic mathematical programming
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| GB/T 7714 | Chu, Li , Wang, Bo , Zhang, Jie et al. CONVERGENCE ANALYSIS OF A SMOOTHING SAA METHOD FOR A STOCHASTIC MATHEMATICAL PROGRAM WITH SECOND-ORDER CONE COMPLEMENTARITY CONSTRAINTS [J]. | JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION , 2021 , 17 (4) : 1863-1886 . |
| MLA | Chu, Li et al. "CONVERGENCE ANALYSIS OF A SMOOTHING SAA METHOD FOR A STOCHASTIC MATHEMATICAL PROGRAM WITH SECOND-ORDER CONE COMPLEMENTARITY CONSTRAINTS" . | JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 17 . 4 (2021) : 1863-1886 . |
| APA | Chu, Li , Wang, Bo , Zhang, Jie , Zhang, Hong-Wei . CONVERGENCE ANALYSIS OF A SMOOTHING SAA METHOD FOR A STOCHASTIC MATHEMATICAL PROGRAM WITH SECOND-ORDER CONE COMPLEMENTARITY CONSTRAINTS . | JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION , 2021 , 17 (4) , 1863-1886 . |
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This paper focuses on efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian. Based on the Lagrangian duality theory, we deal with the projection problem via a semismooth Newton algorithm with line search safeguard, which admits global and locally quadratic convergence, to solve a univariate semismooth equation. Numerical experiments show that our proposed algorithm outperforms favourably the existing state-of-the-art standard solvers and is able to reliably solve very large-scale projection problems. Besides, we derive an explicit expression of a generalized Jacobian of the studied projection, which is an essential component of second-order nonsmooth methods.
Keyword ：
generalized Jacobian generalized Jacobian Projection Projection semismooth Newton method semismooth Newton method
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| GB/T 7714 | Wang, Bo , Lin, Lanyu , Liu, Yong-Jin . Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian [J]. | OPTIMIZATION , 2021 , 71 (4) : 1073-1096 . |
| MLA | Wang, Bo et al. "Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian" . | OPTIMIZATION 71 . 4 (2021) : 1073-1096 . |
| APA | Wang, Bo , Lin, Lanyu , Liu, Yong-Jin . Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian . | OPTIMIZATION , 2021 , 71 (4) , 1073-1096 . |
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In this paper we consider a proximal method of multipliers (PMM) for a nonlinear second-order cone optimization problem. With the assumptions of constraint nondegeneracy, strict complementarity and second-order sufficient condition, we estimate the local convergence rate of PMM to be linear or superlinear, which depends on the strategy of parameter selection.
Keyword ：
Proximal method Proximal method Rate of convergence Rate of convergence Second-order cone Second-order cone
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| GB/T 7714 | Chu, Li , Wang, Bo , Zhang, Liwei et al. The rate of convergence of proximal method of multipliers for second-order cone optimization problems [J]. | OPTIMIZATION LETTERS , 2020 . |
| MLA | Chu, Li et al. "The rate of convergence of proximal method of multipliers for second-order cone optimization problems" . | OPTIMIZATION LETTERS (2020) . |
| APA | Chu, Li , Wang, Bo , Zhang, Liwei , Zhang, Hongwei . The rate of convergence of proximal method of multipliers for second-order cone optimization problems . | OPTIMIZATION LETTERS , 2020 . |
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This paper focuses on perturbation analysis of the conic optimization problem, which is defined as the optimization problem over the epigraph of the weighted norm. The motivation for studying such problem comes from recent interest in the regularized (possibly non-convex) optimization problems arising in a wide variety of fields such as compressive sensing, signal processing and statistical learning. This paper first derives some important geometrical properties of relevant closed convex cone, including the tangent cone, the normal cone and the critical cone. We then show that under the Robinson's constraint qualification, the following conditions are equivalent: the constraint nondegeneracy and the strong second order sufficient optimality condition, the strong regularity of the Karush-Kuhn-Tucker (KKT) point, and the nonsingularity of Clarke's generalized Jacobian of the KKT system, and others. We further provide an important characterization of the isolated calmness for the conic optimization problem, namely, under the Robinson's constraint qualification, the isolated calmness of the KKT solution mapping holds if and only if the strict constraint qualification and the second order sufficient condition hold at a locally optimal solution. These characterizations provide theoretical results to design and analyse efficient algorithms for the conic optimization problem.
Keyword ：
isolated calmness isolated calmness l(1) regularization l(1) regularization perturbation analysis perturbation analysis second order optimality conditions second order optimality conditions strong regularity strong regularity
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| GB/T 7714 | Liu, Yong-Jin , Li, Ruonan , Wang, Bo . On the characterizations of solutions to perturbed l(1) conic optimization problem [J]. | OPTIMIZATION , 2019 , 68 (6) : 1157-1186 . |
| MLA | Liu, Yong-Jin et al. "On the characterizations of solutions to perturbed l(1) conic optimization problem" . | OPTIMIZATION 68 . 6 (2019) : 1157-1186 . |
| APA | Liu, Yong-Jin , Li, Ruonan , Wang, Bo . On the characterizations of solutions to perturbed l(1) conic optimization problem . | OPTIMIZATION , 2019 , 68 (6) , 1157-1186 . |
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Abstract ：
提出了一类带有概率约束的稀疏线性回归模型,一定程度上改善了经典模型的不足.通过概率和数学期望的关系,以及非负实数集合的指示函数可以用两个凸函数之差近似的性质,建立了其保守近似模型,同时建立了近似模型和原模型的最优解集合,稳定点集合之间的收敛关系.为了求解近似模型,利用凸函数差的性质,建立了序列凸近似算法,并证明了其收敛性.注意序列凸近似的子问题是随机优化问题,其中随机变量可以用Monte Carlo随机抽样进行近似.可以证明Monte Carlo近似问题的结果以概率1收敛到序列凸子问题.最后数值实验说明了该方法的有效性.
Keyword ：
概率约束 概率约束 稀疏优化 稀疏优化 线性回归 线性回归
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| GB/T 7714 | 王博 , 初丽 . 一类概率约束稀疏线性回归模型 [J]. | 吉林师范大学学报（自然科学版） , 2019 , 40 (3) : 51-58 . |
| MLA | 王博 et al. "一类概率约束稀疏线性回归模型" . | 吉林师范大学学报（自然科学版） 40 . 3 (2019) : 51-58 . |
| APA | 王博 , 初丽 . 一类概率约束稀疏线性回归模型 . | 吉林师范大学学报（自然科学版） , 2019 , 40 (3) , 51-58 . |
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