报告题目：A Partially Feasible Jacobi-type Distributed SQO Method for Two-block General Linearly Constrained Smooth Optimization

报 告 人：简金宝

报告时间：2025.3.28 下午18：30

报告地点： 莲花街校区惟德楼315会议室

报告人简介

简金宝，西安交通大学理学博士学位，广西民族大学二级教授，博士生导师。

学术研究：长期从事“最优化理论方法及其在电气工程中的应用”研究；先后主持7项国家自然科学基金项目（4项面上），3项广西自然科学基金重点项目和10多项省级项目。2000年以来，以第一作者或第一通信作者身份在高质量期刊上发表研究成果80多篇，如《Journal of Scientific Computing》、《IEEE Transactions on Power Systems》、《European Journal of Operational Research》、《Computational Optimization and Applications》、《Journal of Optimization Theory and Applications》、《Applied Energy》、《中国科学·数学》和《中国电机工程学报》等。

获奖与荣誉：主持完成的4项科研成果先后获得省级科学技术奖二等奖，享受国务院政府特殊津贴（2007），“全国教育系统先进工作者”（2009），广西壮族自治区“优秀专家”（2006第五批，2018年第九批）。

学术兼职： 中国运筹学会第十二届理事会副理事长（2024.10-），中国运筹学会数学规划分会副理事长（2019.05-），广西运筹学会第一届理事会理事长（2011.11-），《计算数学》和《系统科学与数学》等高质量核心期刊现任编委.

报告内容简介

This talk discusses a class of two-block smooth large-scale optimization problems with both linear equality and linear inequality constraints, which have a wide range of applications, such as economic power dispatch, data mining, signal processing, etc.　Our goal is to develop a novel partially feasible distributed (PFD) sequential　quadratic optimization (SQO) method (PFD-SQOM) for this kind of problems. The design of the method is based on the ideas of SQO method and augmented Lagrangian Jacobi splitting scheme as well as feasible direction method, which decomposes the quadratic optimization (QO) subproblem into two small-scale QOs that can be solved independently and parallelly. A novel  disturbance contraction term that can be suitably adjusted is introduced into the inequality constraints so that the feasible step size along the search direction can be increased to 1. The new iteration points are generated by the Armijo line search and the partially augmented Lagrangian function that only contains equality constraints as the merit function. The iteration points always satisfy all the inequality constraints of the problem. The global convergence and iterative complexity of the proposed PFD-SQOM are obtained under appropriate assumptions. Furthermore, the rate of convergence such as superlinear and quadratic rates of convergence of the proposed method are analyzed when the equality　constraint vanishes. Finally, the numerical effectiveness of the method is tested on a class of academic examples and an economic power dispatch problem, which shows that the proposed method is  promising.

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数学与统计学院

2025年3月27日