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# Category Archives: 学术报告

## 美国斯坦福大学叶荫宇教授 8月23日上午做学术报告

Topic: Distrubuted Solvers for Linear Programming

## 美国休斯顿大学彭积明教授 5月22日上午做学术报告

Topic:The Direct Extension of ADMM for Multi-block Convex Minimization Problems is Not Necessarily Convergent

Abstract:

The issue of how to solve generic non-convex QP has been a long standing challenge in optimization. Existing global algorithms usually refer to branch-and-bound or successive relaxation approaches whose running time are typically exponential in term of the number of variables. Moreover, it has been proved that even finding a local optimal solution to LCQP is NP-hard.
In this talk, we introduce a new design paradigm for LCQPs with a few negative eigenvalues that are known to be NP-hard. We first introduce a new class of Lagrangian functions that satisfy the KKT conditions automatically. By using the new Lagrangian function, we present an alternative update scheme to improve the objective function. We then characterize the accumulation point of the sequence. By integrating the new algorithm and other simple optimization techniques such as convex relaxation, line search and partitioning, we present a global algorithm to find the global optimal solution to the underlying LCQP and estimate its complexity. Promising numerical experiments will be reported as well.

## 美国斯坦福大学叶荫宇教授 4月4日上午做学术报告

Topic: Optimization with Uncertain, Online and Massive Data

Abstract:

We present several analytic models and computational algorithms dealing with online/dynamic, structured and/or massively distributed data. Specifically, we discuss ：
• Distributionally Robust Optimization Models, where many problems can be efficiently solved when the associated uncertain data possess no priori distributions;
• Near-Optimal Online Linear Programming Algorithms, where the matrix data is revealed column by column along with the objective function and a decision has to be made as soon as a variable arrives;
•Sparse regression with Non-convex Regularization, where we give sparse and structure characterizations for every KKT stationary solution of the problem;
• Alternating Direction Method of Multipliers (ADMM) for large-scale data, where we give an example to show that the direct extension of ADMM for three-block convex minimization problems is not necessarily convergent, and propose simple and effective convergent variants.

## 优化中心12月13日邀请报告

Topic:  优化算法开源库搭建

Abstract:

Topic: Warmstarting the Homogeneous and Self-Dual Interior Point Method for Linear and Conic Quadratic Problems

Abstract:

We present two strategies for warmstarting primal-dual interior point methods for the homogeneous self-dual model when applied to mixed linear and quadratic conic optimization problems. Common to both strategies is their use of only the final (optimal) iterate of the initial problem and their negligible computational cost. This is a major advantage when compared to previously suggested strategies that require a pool of iterates from the solution process of the initial problem. Consequently our strategies are better suited for users who use optimization algorithms as black-box routines which usually only output the final solution. Our two strategies differ in that one assumes knowledge only of the final primal solution while the other assumes the avail-ability of both primal and dual solutions.We analyze the strategies and deduce conditions under which they result in improved theoretical worst-case complexity. We present extensive computational results showing work reductions when warmstarting compared to coldstarting in the range 30%{75% depending on the problem class and magnitude of the problem perturbation. The computational experiments thus substantiate that the warmstarting strategies are useful in practice.
Joint work with Anders Skajaa and Erling Andersen.

Topic: 计及风电功率波动影响的风电场集群无功电压协调优化控制策略

Abstract:

## 2014年数学规划应用与软件研讨会学术报告

Topic: A class of polynomially solvable 0-1 programming problems and applications

Slides: Modeling01规划2014-Jinxing Xie

Topic: Linearlized Alternating Directions Methods of Multipliers in Sparse Optimization

Abstract:  The problem to find sparse solutions has obtained much attention and well studied widely in the fields of signal processing, compressive sensing, machine learning, statistical inference and so on. The problem mainly formulated as an unconstrained optimization problem which aims to minimize the sum of a smooth function and a non-smooth regularized term, the $\ell_1$-norm regularization, TV regularization, and matrix nuclear norm regularization, for instance. In this talk, we review some recent developed linearized alternating directions methods of multipliers to such problem, give their convergence results, and show their practical performance experimentally.

Slides: Prof. XiaoYunHai Repot_CAS

Topic: 基于矩阵稀疏表示的指纹图像压缩编码算法及软件实现

Topic: 高精度移动通信网络优化规划平台

Abstract:  随着蜂窝移动通信网络的规模不断扩大，无线网络的优化变得日益复杂和困难，仅仅依靠传统的工程优化和规划经验很难提升网络的性能。我们利用数学优化方法，结合电磁波理论，得到了一种高精度场强预测方法，可利用天线参数和地理信息等数据，计算出各天线在每个地理位置的场强值。在此基础上，对于给定的网络性能指标，我们建立了移动通信无线网络天线参数调整的最优化模型，并设计了相应的求解算法，使用该模型和算法可计算出全网或局部网络的天线参数整体优化调整方案。我们把网络性能指标的计算和展示、天线的自动调整和优化等功能编程实现，形成了一套完整的软件系统。该软件可根据使用者的不同需求，设计不同的操作流程以及交互界面，给网络优化工程师提供很好的技术支持。

Topic: 张量的低秩逼近

Abstract:  近年来涌现出许多高维图像数据，其本质上是高阶张量，如果采用传统图像处理方法将张量数据转换为非常长的向量来实现，这样测量就需要非常大样本矩阵，从而带来了巨大的计算和存储负担，同时，也会丧失张量所固有的几何、统计以及非线性度量性质。因此，将传统的理论方法拓展到高阶张量情形成为了亟待解决又非常具有挑战的一个崭新研究课题。本报告首先介绍张量计算，特别是张量低秩逼近计算的国内外研究现状，然后汇报我们的研究团队在张量低秩逼近方面的研究工作，主要包括低秩张量的完备化方法、对称复张量的最佳复秩1逼近的计算方法。

Slides: 张量的低秩逼近-Minru Bai

Topic: 混合整数规划算法与软件

Abstract:  许多实际问题可以归结为混合整数规划问题。比如，火车或飞机调度、工人排班、生产计划、发电机组组合、通讯中设备选址等。常见的混合整数规划问题有指派问题，0-1背包问题、设备覆盖问题、旅行商问题等。混合整数规划常用的算法包括: 预处理、分支定界、割平面、启发式算法等。此方面的软件也有很多，常用的商业软件有: Cplex、Gurobi、Xpress-MP等；常见的非商业软件有: Bonmin、Scip、Knitro等。虽然算法与软件都已经比较成熟，仍有很多问题值得思考。比如，如何针对特殊问题设计算法，如何提高算法的计算效率等。

Slides: 混合正数规划的算法与软件-Prof.Dai

Topic: 优化算法开源库搭建

Abstract:

## Professor Jingyun Yuan from Federal University of Parana, Brazil will be invited to give a talk

Title:

Some Research Methodologies in Applied and Computational Mathematics

## 2014年“优化与应用”学术研讨会会议报告四

Topic:  Implementation of derivative-free optimization algorithms on land subsidence control problems

Abstract:  Due to surface water scarcity and contamination problems, groundwater has been exploited as an important water resource in many areas. However, the extensive pumping causes severe problems. In the Hang Jia Hu plain, land subsidence induced by groundwater extraction from a large number of pumping wells causes flooding, disrupted river navigation and waterlogging of soil, among other problems. In order to mitigate the hazards caused by land subsidence and also meet the domestic and industrial demands for water resources, groundwater exploitation management needs to reply on optimization techniques to determine the most effective strategies. However, this complex groundwater management problem is challenging, as its objective functions being nonsmooth, nonlinear, and having many local minima and lacking derivative forms. In our study, we apply the DYCORS algorithm, which is a derivative free optimization algorithm for solving expensive black-box objective functions. It is based on the radial basis function (RBF) surrogate model and combined with dynamic coordinate search so it is specifically suitable for high dimensional problems. With this optimization and simulation system, we will be able to provide efficient groundwater exploitation management plans under different practical requirements.

## 2014年“优化与应用”学术研讨会会议报告三

Topic:  一个新的非线性规划内点方法

Abstract: 内点方法是求解非线性规划的一类重要方法。传统的内点方法是通过求解松弛KKT条件的拟牛顿方程来产生迭代搜索方向，并通过选取适当的步长来保证迭代点总是内点。这样做有三个明显的缺陷：一是求解半定规划时需要使用对称化技术，导致算法十分复杂；二是为了保证内点可导致一个好的迭代步被截断；三是对于不满足MFCQ或LICQ的问题，Lagrange乘子估计会是无界的。我们提出一类新的内点方法，每次迭代求解一个带有两个参数的原始对偶方程，并能克服上述缺陷。我们将给出算法的全局和局部收敛性分析，并讨论一些相关的话题。一个数值例子表明对于不满足MFCQ或LICQ的问题我们能够获得较高精度的解。

## 2014年“优化与应用”学术研讨会会议报告二

Topic: S-lemma with equality and its applications

Abstract:   Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we overcome the difficulty that the equality $h(x)=0$ does not possess any Slater point and that both $f$ and $h$ may not be homogeneous. We show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any assumption. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots,h_p(x)):~x\in\Bbb R^n\}$ for $f$ being nonhomogeneous and $h_1,\ldots,h_p$ linear can be characterized using the newly developed S-lemma with equality.

## 2014年“优化与应用”学术研讨会会议报告一

Topic:  稀疏非线性优化

Abstract:  稀疏非线性优化是指在一般非线性约束条件下，求一个决策向量使其非零元素的个数达到极小。它是最优化领域中一个前沿且富有挑战性的研究课题，属于运筹学、统计学、管理科学、计算机科学、信息科学等学科的交叉与融合，具有重要的学术意义和广泛的应用背景。这个报告主要介绍稀疏非线性优化模型与基本概念、基本理论包括最优性条件、一阶和二阶算法，以及未来的工作与思考。

Joint work with  潘丽丽，韩继业。