Analysis of optimal boundary control for a three-dimensional reaction-diffusion system
Wanli Yang Jie Sun Su Zhang

This paper is concerned with optimal boundary control of a three dimensional reaction-diffusion system in a more general form than what has been presented in the literature. The state equations are analyzed and the optimal control problem is investigated. Necessary and sufficient optimality conditions are derived. The model is widely applicable due to its generality. Some examples in applications are discussed.

keywords: Optimal control reaction-diffusion system optimality conditions
On analyzing and detecting multiple optima of portfolio optimization
Yue Qi ZhiHao Wang Su Zhang

Portfolio selection is widely recognized as the birth-place of modern finance; portfolio optimization has become a developed tool for portfolio selection by the endeavor of generations of scholars. Multiple optima are an important aspect of optimization. Unfortunately, there is little research for multiple optima of portfolio optimization. We present examples for the multiple optima, emphasize the risk of overlooking the multiple optima by (ordinary) quadratic programming, and report the software failure by parametric quadratic programming. Moreover, we study multiple optima of multiple-objective portfolio selection and prove the nonexistence of the multiple optima of an extension of the model of Merton. This paper can be a step-stone of studying the multiple optima.

keywords: Multiple-objective optimization portfolio optimization multiple optimal solutions multiple efficient solutions parametric quadratic programming
A mathematical model for hepatitis B with infection-age structure
Suxia Zhang Xiaxia Xu
A model with age of infection is formulated to study the possible effects of variable infectivity on HBV transmission dynamics. The stability of equilibria and persistence of the model are analyzed. The results show that if the basic reproductive number $\mathcal{R}_0<1$, then the disease-free equilibrium is globally asymptotically stable. For $\mathcal{R}_0>1$, the disease is uniformly persistent, and a Lyapunov function is used to show that the unique endemic equilibrium is globally stable in a special case.
keywords: stability uniform persistence. age of infection Mathematical model hepatitis B
On linear convergence of projected gradient method for a class of affine rank minimization problems
Yu-Ning Yang Su Zhang
The affine rank minimization problem is to find a low-rank matrix satisfying a set of linear equations, which includes the well-known matrix completion problem as a special case and draws much attention in recent years. In this paper, a new model for affine rank minimization problem is proposed. The new model not only enhances the robustness of affine rank minimization problem, but also leads to high nonconvexity. We show that if the classical projected gradient method is applied to solve our new model, the linear convergence rate can be established under some conditions. Some preliminary experiments have been conducted to show the efficiency and effectiveness of our method.
keywords: Linear convergence affine rank minimization problems. projected gradient method
A variational inequality approach for constrained multifacility Weber problem under gauge
Jianlin Jiang Shun Zhang Su Zhang Jie Wen

The classical multifacility Weber problem (MFWP) is one of the most important models in facility location. This paper considers more general and practical case of MFWP called constrained multifacility Weber problem (CMFWP), in which the gauge is used to measure distances and locational constraints are imposed to facilities. In particular, we develop a variational inequality approach for solving it. The CMFWP is reformulated into a linear variational inequality, whose special structures lead to new projection-type methods. Global convergence of the projection-type methods is proved under mild assumptions. Some preliminary numerical results are reported which verify the effectiveness of proposed methods.

keywords: Facility location multifacility Weber problem gauge locational constraints variational inequality approach

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