Control parametrization and finite element method for controlling multi-species reactive transport in a circular pool
Heung Wing Joseph Lee Chi Kin Chan Karho Yau Kar Hung Wong Colin Myburgh
Journal of Industrial & Management Optimization 2013, 9(3): 505-524 doi: 10.3934/jimo.2013.9.505
In this paper, we consider an optimal control problem for a cleaning program involving effluent discharge of several species in a circular pool. A computational scheme combining control parametrization and finite element method is used to develop a cleaning program to meet the environmental health requirements. A numerical example is solved to illustrate the efficiency of our method.
keywords: Galerkin Scheme Species concentration control parametrization circular pool non-negativity requirement of state variables. optimal control
Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels
Kar Hung Wong Yu Chung Eugene Lee Heung Wing Joseph Lee Chi Kin Chan
Journal of Industrial & Management Optimization 2018, 14(3): 877-894 doi: 10.3934/jimo.2017080

This paper considers an optimal production scheduling problem in a single-supplier-multi-manufacturer supply chain involving production and delivery time-delays, where the time-delays for the supplier and the manufacturers can have different values. The objective of both levels is to find an optimal production schedule so that their production rates and their inventory levels are close to the ideal values as much as possible in the whole planning horizon. Each manufacturer's problem, which involves one time-delayed argument, can be solved analytically by using the necessary condition of optimality. To tackle the supplier's problem involving $n+1$ different time-delayed arguments (where $n$ is the number of manufacturers) by the above approach, we need to introduce a model transformation technique which converts the original system of combined algebraic/differential equations with $n+1$ time-delayed arguments into a sum of $n$ sub-systems, each of which consists of only two time-delayed arguments. Thus, the supplier's problem can also be solved analytically. Numerical examples consisting of a single supplier and four manufacturers are solved to provide insight of the optimal strategies of both levels.

keywords: Optimal control supply chain problem single-supplier multimanufacturer time delays in the production process multiple time delays
Strong duality theorem for multiobjective higher order nondifferentiable symmetric dual programs
Xinmin Yang Jin Yang Heung Wing Joseph Lee
Journal of Industrial & Management Optimization 2013, 9(3): 525-530 doi: 10.3934/jimo.2013.9.525
In this paper, we establish a strong duality theorem for Mond-Weir type multiobjective higher order nondifferentiable symmetric dual programs. Our works correct some deficiencies in recent papers [higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290(2004)423-435] and [A note on higher-order nondifferentiable symmetric duality in multiobjective programming, Appl. Math. Letters 24(2011) 1308-1311].
keywords: nondifferentiablity. strong duality theorem Multiobjective programming higher order Mond-Weir symmetric dual model
On saddle points of a class of augmented lagrangian functions
Qian Liu Xinmin Yang Heung Wing Joseph Lee
Journal of Industrial & Management Optimization 2007, 3(4): 693-700 doi: 10.3934/jimo.2007.3.693
For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.
keywords: augmented Lagrangian function. saddle point Nonconvex optimization

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