学术报告题目和摘要

显著性研究方法

刘秀平（大连理工大学）

近年来，随着计算机视觉技术的发展，显著性检测问题备受关注。显著性方法不仅为图形图像处理，如分割、图像放缩等提供了新的技术和手段,也为数字网格技术的研究带来了新的机遇和挑战。本报告主要针对二部分内容展开介绍.一部分是关于图像显著性问题,主要介绍新近的研究成果,如基于马尔科夫吸收概率的显著性方法和基于模式挖掘的显著种子检测方法.另一部分内容是针对三维网格的显著性问题,介绍新近的研究成果，如随机游走方法和流行排序方法等。

B-spline Surface Fitting with Knot Position Optimization

曹娟（hg8868官方网站）

In linear least squares fitting of B-spline surfaces, the choice of knot vector is essentially important to the quality of the approximating surface. In this paper, a heuristic criterion for optimal knot positions in the fitting problem is formulated as an optimization problem according to the geometric feature distribution of the input data. Then, the coordinate descent algorithm is used for the optimal knot computation. Based on knot position optimization, an iterative surface fitting framework is developed, which adaptively introduces more knot isolines passing through the regions with more complex geometry or large fitting errors. Hence, the approximation quality of the reconstructed surface is progressively improved up to a pre-specified threshold. We test several models to demonstrate the efficacy of our method in fitting surface with distinct geometric features. Different from the knot placement technique (NKTP method) and the dominant-column- based fitting method (DOM-based method) which require input data in semi-grid or grid form, our algorithm takes more general data points as input, i.e., any scattered data sets with parameterization. Comparing to NKTP method and DOM-based method, our method efficiently produces more accurate results by using the same number of knots.

Isolated Calmness for Convex Composite Quadratic and Semi-Definite   Programming

张立卫（大连理工大学）

This report first gives a literature review for the stability of optimization problems. After that I discuss the  isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping  for nonlinear semi-definite programming at a locally optimal solution. Finally we give characterizations of the isolated calmness of KKT mapping for convex composite quadratic and semi-definite programming. (This is a joint work with Deren Han and Defeng Sun)。

Necessary optimality conditions for a class of optimal control problems with nonsmooth mixed constraints

李安（hg8868官方网站）

We study a class of optimal control problems with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints are derived under the Mangasarian-Fromovitz Condition and under the assumption that the state and control constraint functions are smooth. We derive the necessary optimality conditions for optimal control problems with nonsmooth mixed constraints under weaker constraint qualifications based on pseudo-Lipschitz continuity and calmness of certain set-valued maps. Finally we apply these optimality conditions to bilevel optimal control problems with finite-dimensional lower level. We combine the classical KKT conditions and value function approaches to get new necessary optimality conditions.

Some Whyburn type limit theorems and their applications

代国伟（大连理工大学）

In this topic, we present several Whyburn type limit theorems. As applications, we investigate the existence and multiplicity of one-sign solutions of p-Laplacian problem involving a linear/superlinear nonlinearity with zeros. Moreover, we also introduce some global bifurcation theorems for nonlinear operator equation with homogeneous operator.

Modeling clustered long-term survivors using marginal models

牛一 （大连理工大学）

Clustered survival time data often arise in biomedical and clinical studies where potential correlation among survival times is induced in a cluster. Another important feature of failure time data is a possible fraction of cured subjects. In this talk, we consider a semiparametric marginal mixture cure model for right censored clustered failure time data in a likelihood-based context. We propose a novel estimating equation approach to explicitly model the association among the survival times of uncured patients and the dependence among the cure statuses. We derive the large sample properties of the regression estimators. The finite sample studies demonstrate the good applicability of the proposed method.

A Riemannian Inexact Newton-CG Method for Nonnegative Inverse Eigenvalue Problems: Nonsymmetric Case

白正简（hg8868官方网站）

In this talk, we consider the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We reformulate the nonnegative inverse eigenvalue problem as an underdetermined constrained nonlinear matrix equation over several matrix manifolds. Then we propose a Riemannian inexact Newton-CG method for solving the nonlinear matrix equation. The global and quadratic convergence of the proposed method is established. Finally, we report some numerical experiments to illustrate the efficiency of the proposed method.

一类分布鲁棒最优控制问题的初探

王磊（大连理工大学）

We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as the worst-case expectation over a set of possible distributions of the uncertain parameter. This ambiguity set of distributions is, in turn, defined by the first two moments of the random variables involved. The optimal control is found by minimizing the worst-case expectation over all possible distributions in this set. If the distributions are discrete, the stochastic min-max optimal control problem can be converted into a conventional optimal control problem via duality, which is then approximated as a finite-dimensional optimization problem via the control parametrization. We derive necessary conditions of optimality and propose an algorithm to solve the approximation optimization problem. The results of discrete probability distribution are then extended to the case with one dimensional continuous stochastic variable by applying the control parametrization methodology on the continuous stochastic variable, and the convergence results are derived. A numerical example is present to illustrate the potential application of the proposed model and the effectiveness of the algorithm.