A variational inequality approach for constrained multifacility Weber problem under gauge
Jianlin Jiang Shun Zhang Su Zhang Jie Wen
Journal of Industrial & Management Optimization 2018, 14(3): 1085-1104 doi: 10.3934/jimo.2017091

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
On analyzing and detecting multiple optima of portfolio optimization
Yue Qi Zhihao Wang Su Zhang
Journal of Industrial & Management Optimization 2018, 14(1): 309-323 doi: 10.3934/jimo.2017048

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
Analysis of optimal boundary control for a three-dimensional reaction-diffusion system
Wanli Yang Jie Sun Su Zhang
Numerical Algebra, Control & Optimization 2017, 7(3): 325-344 doi: 10.3934/naco.2017021

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
Double projection algorithms for solving the split feasibility problems
Ya-zheng Dang Jie Sun Su Zhang
Journal of Industrial & Management Optimization 2017, 13(5): 1-12 doi: 10.3934/jimo.2018135

We propose two new double projection algorithms for solving the split feasibility problem (SFP). Different from the extragradient projection algorithms, the proposed algorithms do not require fixed stepsize and do not employ the same projection region at different projection steps. We adopt flexible rules for selecting the stepsize and the projection region. The proposed algorithms are shown to be convergent under certain assumptions. Numerical experiments show that the proposed methods appear to be more efficient than the relaxed- CQ algorithm.

keywords: Armijo-type line search convergence analysis double projection algorithm optimization split feasibility problem
Immediate schedule adjustment and semidefinite relaxation
Jinling Zhao Wei Chen Su Zhang
Journal of Industrial & Management Optimization 2019, 15(2): 633-645 doi: 10.3934/jimo.2018062

This paper considers the problem of temporary shortage of some resources within a project execution period. Mathematical models for two different cases of this problem are established. Semidefinite relaxation technique is applied to get immediate solvent of these models. Relationship between the models and their semidefinite relaxations is studied, and some numerical experiments are implemented, which show that these mathematical models are reasonable and feasible for practice, and semidefinite relaxation can efficiently solve the problem.

keywords: Schedule adjustment immediate resource-constrained semidefinite relaxation

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