2018 连续优化专题研讨会

辽宁 大连

2018 年8 月5-7 日

主办单位：

承办单位：

目录

委员会成员表 .................................................................................... 1

组织委员会 .................................................................................... 1

会议日程简表 .................................................................................... 2

会议报告详细信息 ............................................................................... 3

参会人员通讯录 ............................................................................... 11

2018 连续优化专题研讨会

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委员会成员表

组织委员会

主任：张立卫

委员：刘勇进

肖现涛

张晓军

秘书：吴 佳

张赛楠

2018 连续优化专题研讨会

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会议日程简表

会议地址：星海高尔夫酒店三楼报告厅

2018 年8 月5 日（星期日）10:00-21:30 报到 地点：星海高尔夫酒店大堂

会议报到注册信息联系人：张赛楠

2018 年8 月5 日（星期日）18:00-20:00 晚餐 地点：星海高尔夫酒店

2018 年8 月6 日（星期一）8:00-12:00 地点：星海高尔夫酒店

08:00-08:15 开幕式

08:15-08:30 合影

08:30-10:10 特邀报告（4 个）

每个报告25 分钟，20 分钟报告，5 分钟提问

10:10-10:20 茶歇休息

10:20-11:35 特邀报告（3 个）

每个报告25 分钟，20 分钟报告，5 分钟提问

12:00-14:00 午餐 地点：星海高尔夫酒店

2018 年8 月6 日（星期一）14:00-17:40 地点：星海高尔夫酒店

14:00-17:40 特邀报告（8 个）

每个报告25 分钟，20 分钟报告，5 分钟提问

18:00-20:00 晚餐 地点：星海高尔夫酒店

2018 年8 月7 日（星期二）08:30-17:00 地点：3003新葡官方网站

08:30-17:00 自由讨论

2018 连续优化专题研讨会

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会议报告详细信息

8 月6 日上午

开幕式及大会报告 地点：星海高尔夫酒店

时间 会议内容及报告题目 报告人 主持人

08:00-08:15 开幕式 张晓军

08:15-08:30 合影

08:30-08:55 The optimization problem in MIMO radar transmit

beampattern matching design

张晓军

08:55-09:20 Efficient sparse Hessian based algorithms for the 金丽

clustered lasso problem

刘勇进

09:20-09:45 An efficient Hessian based algorithm for solving

large-scale sparse group Lasso problems

张宁

09:45-10:10 Quantitative stability analysis for parametric

optimization problems and applications

张杰

10:10-10:20 茶歇休息

10:20-10:45 Stochastic first- and second-order methods for

nonsmooth stochastic programs

肖现涛

10:45-11:10 A study of a DC penalty formulation for solving a class of 刘勇进

quadratic programs with linear complementarity constraints

吴佳

11;10-11:35 Properties associated with the epigraph of the norm

function of projection onto the nonnegative orthant

王莉

午餐12:00-14:00，地点：星海高尔夫酒店

8 月6 日下午

大会报告 地点：星海高尔夫酒店

14:00-14:25 Recent Progress on Non-Symmetric Cones 卢越

张杰

14:25-14:50 A Class of Smooth Approximation Methods for

Solving Chance Constrained Optimization Problems

任咏红

14:50-15:15 A neural network based on two discrete-type

complementarity functions for solving SOCQP and SOCCVI

孙菊贺

15:15-15:40 中国交通拥堵收费的接受性与治理效果研究 袁艳红

15:40-16:00 茶歇休息

16:00-16:25 A smoothing method for mathematical programs with

complementarity constraints

贺素香

16:25-16:50 A smoothing method for a class of generalized Nash 肖现涛

equilibrium problems

侯剑

16:50-17:15 New Constraint Qualifications and Optimality

Conditions for Second Order Cone Programs

张艺

17:15-17:40 A smoothing SAA method for a stochastic mathematical

program with SOC complementarity constraints

王博

2018 连续优化专题研讨会

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报告题目与摘要

贺素香

A smoothing method for mathematical programs with

complementarity constraints

报告摘要

This paper presents a smoothing method for mathematical programs with

complementarity constraints (MPCC) based on the integral of the sigmoid

function. The original MPCC is reformulated as a standard smooth

approximation minimization problem with a smooth parameter and the

approximate solution of the MPCC is obtained by solving a series of the

smooth subproblems with the smooth parameter approaching to zero. The

characterizations of the linear independence constraints qualification (LICQ),

the KKT condition and the second-order sufficient condition for the smooth

approximation problem are established under several assumptions on the

original MPCC, which ensures the existence of KKT stationary solutions to the

smooth subproblems. Furthermore, it is proven that the accumulation point of

sequence of KKT stationary solutions to the smooth subproblems is a

C-stationary point of the MPCC under the weaker assumptions, without

asymptotically weakly nondegenerate (AWN) condition. At last, we implement

numerical experiments to test the efficiency of the proposed smoothing

method by solving some typical problems in MacMPEC database. The

reported numerical results show that the proposed smoothing method is

promising by comparing with the other related method and the optimal values

in MacMPEC database.

侯剑

A smoothing method for a class of generalized Nash equilibrium

problems

报告摘要

The generalized Nash equilibrium problem is an extension of the standard

Nash equilibrium problem where both the utility function and the strategy

space of each player depend on the strategies chosen by all other players.

Recently, the generalized Nash equilibrium problem has emerged as an

effective and powerful tool for modeling a wide class of problems arising in

many fields and yet solution algorithms are extremely scarce. In this paper,

using a regularized Nikaido-Isoda function, we reformulate the generalized

Nash equilibrium problem as a mathematical program with complementarity

constraints (MPCC). We then propose a suitable method for this MPCC and

under some conditions, we establish the convergence of the proposed method

2018 连续优化专题研讨会

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by showing that any accumulation point of the generated sequence is a

M-stationary point of the MPCC. Numerical results on some generalized Nash

equilibrium problems are reported to illustrate the behavior of our approach.

刘勇进

Efficient sparse Hessian based algorithms for the clustered lasso

problem

报告摘要

In this talk, we focus on solving the clustered lasso problem, which is a least

square problem with the L1-type penalties imposed on both the coefficients

and their pairwise differences to learn the group structure of the regression

parameters. This work first reformulates the clustered lasso regularizer as a

weighted sorted-lasso regularizer, which takes much lower computational cost

than the original one. This work then proposes an inexact semismooth Newton

augmented Lagrangian (Ssnal) algorithm to solve this equivalent reformulation

or its dual depending on whether the sample size is larger than the dimension

of the features. Comprehensive results on the global convergence and local

convergence rate of the Ssnal algorithm are established. For the purpose of

exposition and comparison, this work also summarizes/designs several

first-order methods that can be applied to solve the problem under

consideration. The numerical experiments show that the Ssnal algorithm

substantially outperforms the best alternative algorithms for the clustered lasso

problems. [This is a joint work with Meixia Lin, Defeng Sun and Kim-Chuan

Toh.]

卢越

Recent Progress on Non-Symmetric Cones

报告摘要

Non-symmetric cones have long been mysterious to optimization

researchers because of no unified analysis technique to handle these cones.

Nonetheless, by looking into symmetric cones and non-symmetric cones, it is

still possible to find relations between these kinds of cones. More specifically,

projections onto cones, spectral decomposition associated with cones,

non-smooth analysis regarding cone-functions and cone-convexity are the

bridges between symmetric cone programs and non-symmetric cone

programs. This talk is to present some recent progress on non-symmetric

cones in views of these items. We believe that all the aforementioned results

are very crucial to subsequent study on non-symmetric conic programming.

2018 连续优化专题研讨会

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任咏红

A Class of Smooth Approximation Methods for Solving Chance

Constrained Optimization Problems

报告摘要

Many practical problems with important sig, such as calculation of risk

value in risk optimization, systemic scheduling problem with new energy and

power, route location processing in mobile networks, and so on, belong to

probabilistic constrained optimization problem, which requires that random

constraints should be satisfied with a large enough probability Simultaneously.

Representative methods are convex conservative approximation method, D.C.

approximation method, smooth approximation method, etc. In view of

non-differentiability of probability constrained functions, a class of smooth

approximation methods for solving chance constrained optimization problems

is discussed in this paper. Theoretical framework and algorithm design are

built. Firstly, a class of smooth approximation functions to characteristic

function is defined, and the corresponding smooth approximation problems

(På ) are established. Secondly, sequence convex approximation algorithm is

proposed to solve the smooth approximation problems. Finally, numerical

results based on Pinar-Zenios smooth sum function and Sigmoid function are

reported respectively. The numerical results illustrate that the proposed

smooth approximation method is effective for solving some chance

constrained optimization problems.

孙菊贺

A neural network based on two discrete-type complementarity

functions for solving SOCQP and SOCCVI

报告摘要

This paper focuses on solving the quadratic programming problems with

second-order cone constraints (SOCQP) and the second-order cone

constrained variational inequality (SOCCVI) by using the neural network. More

specifically, a neural network model based on two discrete-type

complementarity functions associated with second-order cone, which are

discovered recently, is proposed to deal with the Karush-Kuhn-Tucker (KKT)

conditions of SOCQP and SOCCVI. Under some condition, the Lyapunov

stability, asymptotical stability, and exponential stability is established,

2018 连续优化专题研讨会

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respectively. Some simulation results are provided to demonstrate the

effectiveness of the proposed neural network.

王博

A smoothing SAA method for a stochastic mathematical program

with second-order cone complementarity constraints

报告摘要

To solve a stochastic mathematical program with second order cone

complementarity constraints, we suggest a smoothing SAA approach. We first

construct a surrogate SAA problem with a projection operator. Smoothing

technique is then employed. Under some mild assumptions, we proved that

our approach convergence to the proposed C-stationary almost surly, and with

additional assumptions, M-stationary and S-stationary can be achieved almost

surly.

王莉

Properties associated with the epigraph of the 1 l norm function of

projection onto the nonnegative orthant

报告摘要

This paper studies some properties associated with a closed convex cone ê1+ ,

which is defined as the epigraph of the 1 l norm function of the metric

projection onto the nonnegative orthant. Specifically, this paper presents some

properties on variational geometry of ê1+ such as the dual cone, the tangent

cone, the normal cone, the critical cone and its convex hull, and others; as well

as the differential properties of the metric projection onto ê1+ including the

directional derivative, the B-subdifferential, and the Clarke’s generalized

Jacobian. These results presented in this paper lay a foundation for future

work on sensitivity and stability analysis of the optimization problems over ê1+ .

吴佳

A study of a DC penalty formulation for solving a class of quadratic

programs with linear complementarity constraints

报告摘要

In this paper, we study a type of DC penalty formulation based on a piecewise

linear penalty function for computing stationary solutions of quadratic

programs with linear complementarity constraints (QPCCs). Relationships

between the stationary points of the QPCC and those of the penalty

formulation, especially for fixed values of the penalty parameter, are discussed.

2018 连续优化专题研讨会

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The associated difference-of-convex algorithm is applied to solve the penalty

formulation.

肖现涛

Stochastic First- and Second-Order Methods for Nonsmooth Stochastic

Programs

报告摘要

In this talk, I will introduce some recent work on stochastic optimization

methods. In the first part, the convergence analysis of stochastic gradient-type

methods without variance uniformly bounded condition will be presented. In

the second part, the global and local convergence of a stochastic semismooth

Newton method will be discussed.

袁艳红

中国交通拥堵收费的接受性与治理效果研究

报告摘要

征收交通拥堵费是近年来我国大型城市考虑试行的交通拥堵治理方案，然而这项

费用的提出目前存在一定社会争议。本文旨在对施行此方案的效果和影响进行全

面预测与分析，以期为有关部门提供政策依据。文章基于人均可支配收入、居民

人口数量、GDP、私家车保有量、空气二氧化硫含量这五种主要影响因素，建立

了征收交通拥堵费的系统动力学模型，然后将人口迁入量作为居民反应的度量指

标，将私家车出行量作为方案实施效果的度量指标，借助北京市相关数据进行了

仿真和分析。经研究得出，高收入水平居民对是否实行拥堵收费政策最敏感，低

收入水平居民对交通拥堵收费的价格高低最敏感。在方案实施初期，私家车出行

增加量虽然确实大幅减少，但出行量的增长速度却明显加快。方案实施稳定后，

私家车出行量的增长速度将趋于方案实施前的增长速度，出行量小于方案实施前，

达到了降低出行量的目的。此外，居民收入水平越高，其表现越稳定，表现在私

家车出行量受拥堵收费影响较小和出行量的增长速度变化越小。

张杰

Quantitative stability analysis for parametric optimization problems and

applications

报告摘要

Quantitative stability analysis for a deterministic parametric minimization

problem with cone constraints are carried out. Under the Slater constraint

2018 连续优化专题研讨会

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qualification, we derive continuity for the feasible solution set mapping and the

optimal solution set mapping against variation of the parameter over Banach

space. In comparison with the existing stability results for parametric

programming, our results are established without any assumption on

continuous differentiability of the underlying functions or reducibility of K.

The results established are applied to stability analysis of a distributionally

robust optimization、stability analysis of a stochastic quasi-variational

inequality and convergence analysis of a global algorithm for a nonconvex

QCQP.

张宁

An efficient Hessian based algorithm for solving large-scale sparse

group Lasso problems

报告摘要

The sparse group Lasso is a widely used statistical model which encourages

the sparsity both on a group and within the group level. In this paper, we

develop an efficient augmented Lagrangian method for large-scale

non-overlapping sparse group Lasso problems with each subproblem being

solved by a superlinearly convergent inexact semismooth Newton method.

Theoretically, we prove that, if the penalty parameter is chosen sufficiently

large, the augmented Lagrangian method converges globally at an arbitrarily

fast linear rate for the primal iterative sequence, the dual infeasibility, and the

duality gap of the primal and dual objective functions. Computationally, we

derive explicitly the generalized Jacobian of the proximal mapping associated

with the sparse group Lasso regularizer and exploit fully the underlying second

order sparsity through the semismooth Newton method. The efficiency and

robustness of our proposed algorithm are demonstrated by numerical

experiments on both the synthetic and real data sets.

张晓军

The optimization problem in MIMO radar transmit beampattern

matching design

报告摘要

In this talk, a novel transmit beampattern matching design method is proposed

for a multiple-input multiple-output (MIMO) radar system. Whereas previous

approaches first solve the correlation matrix R, then use R to design the

transmit signal S, the proposed one-step method obtains the transmit signal S

directly through solving the waveform matrix P. Since MIMO radar transmit

beampattern matching design is an inverse problem of the transmit

beampattern, in this paper, we first discuss some important properties of the

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transmit beampattern and standardize the beampattern matching design

problem. We then theoretically explain the value of the signal waveform matrix

P, followed by an unconstrained optimization problem to solve P. Numerical

examples demonstrate the advantages of the proposed one-step method for

the MIMO radar transmit beampattern matching design problem, including

uniform and non-uniform linear arrays.

张艺

New Constraint Qualifications and Optimality Conditions for

Second Order Cone Programs

报告摘要

We introduce three new constraint qualifications for nonlinear second order

cone programming problems that we call constant rank constraint qualification,

relaxed constant rank constraint qualification and constant rank of the

subspace component condition. Our development is inspired by the

corresponding constraint qualifications for nonlinear programming problems.

We provide proofs and examples that show the relations of the three new

constraint qualifications with other known constraint qualifications. In particular,

the new constraint qualifications neither imply nor are implied by Robinson's

constraint qualification, but they are stronger than Abadie's constraint

qualification. First order necessary optimality conditions are shown to hold

under the three new constraint qualifications, whereas the second order

necessary conditions hold for two of them, the constant rank constraint

qualification and the relaxed constant rank constraint qualification.

2018 连续优化专题研讨会