“运筹学基础与发展论坛”系列活动

主讲嘉宾：Boris Mordukhovich教授（Wayne State University）

    Boris Mordukhovich，美国韦恩州立大学杰出大学教授， 1973年获白俄罗斯国立大学博士学位。他是现代变分分析的奠基人之一，对变分分析理论做出了重大贡献，并将其理论应用于优化、最优控制和数理经济学等诸多领域，发表了大量学术论文及专著。当选为美国数学学会会士（AMS Fellow）和美国工业与应用数学学会会士（SIAM Fellow），并且获得了许多国际奖项。创办了期刊Set-Valued Var. Anal.，也是诸多顶级期刊的编委，并且名列数学高被引学者。

课程材料

VARIATIONAL ANALYSIS: AN OVERVIEW

CRITICALITY OF LAGRANGE MULTIPLIERS IN CONSTRAINED OPTIMIZATION WITH APPLICATIONS TO SQP

PARABOLIC REGULARITY IN VARIATIONAL ANALYSIS AND OPTIMIZATION

GLOBALLY CONVERGENT CODERIVATIVE-BASED NEWTONIAN ALGORITHMS IN NONSMOOTH OPTIMIZATION

OPTIMAL CONTROL OF SWEEPING PROCESSES WITH APPLICATIONS TO ROBOTICS AND TRAFFIC EQUILIBRIA

课程回放

https://space.bilibili.com/1254993141/

Topic: VARIATIONAL ANALYSIS IN OPTIMIZATION AND CONTROL

This course consists of five lectures devoted to advanced tools of variational analysis and generalized differentiation with their applications to qualitative and algorithmic aspects of optimization theory and optimal control.

 

Variational Analysis: An Overview

2021年11月16日21：30--23：00

This lecture contains a brief overview of basic principles and constructions of variational analysis and generalized differentiation with reviewing some underlying results and areas of applications. In particular, we axiomatically define subdifferentials of nonsmooth functions and normal to closed sets with their major realizations, present the extremal principle and its applications to generalized Lagrange multiplier rules, and formulate necessary optimality conditions for general problems of optimal control.

 

Criticality of Lagrange Multipliers in Constrained Optimization with Applications to SQP

2021年11月17日21：30--23：00

This lecture is devoted to a new theory of critical and noncritical Lagrange multipliers for general problems of constrained optimization, including conic programming. Using advanced machinery of variational analysis, a generalized differentiation, we present second-order characterizations of critical and noncritical multiplies with their applications to the sequential quadratic programming method (SQP) in problems of constrained optimization.

Parabolic Regularity in Variational Analysis and Optimization

2021年11月18日21：30--23：00

In this lecture we discuss some basic notions of second-order variational analysis that are revolved around the concept of parabolic regularity for functions and sets. This general second-order regularity concept plays a fundamental role in deriving a variety of second-order calculus rules for primal and dual constructions of generalized differentiation and their applications including necessary and sufficient optimality conditions for various problems of constrained optimization, uniform growth conditions for augmented Lagrangians in conic programming, etc.

Globally Convergent Coderivative-based Newtonian Algorithms in Nonsmooth Optimization

2021年11月19日21：30--23：00

This lecture is devoted to applications of second-order variational analysis and generalized differentiation to the design and justification of novel generalized Newtonian algorithms. We present coderivative-based versions of the damped Newton method and of the Levenberg-Marquardt method designed via the generalized Hessian. Efficient conditions for the global convergence of these algorithms are obtained for problems of convex composite optimization with establishing their superlinear convergence rates and applications to Lasso problems.

 

Optimal Control of Sweeping Process with Applications to Robotics and Traffic Equilibria

2021年11月20日21：30--23：00

The final lecture of this course is devoted to applications of variational analysis to a new and challenging class of optimal control problems for the so-called sweeping processes, which are governed by discontinuous differential inclusions, dynamic variational inequalities. We develop the method of finite-difference/discrete approximations to the study of such problems and then derive in this way necessary optimality conditions for discrete-time and continuous-time systems with applications to some models of robotics and traffic equilibria.