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101.
K. L. Teo 《Numerical Functional Analysis & Optimization》2013,34(2-3):125-144
In this paper, we consider a class of Optimal Control problems involving first boundary value problems of parabolic type. A strong variational algorithm has been obtained for solving this class of optimal control problems in a paper by the author and D. W. Reid. It was also shown that any L∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problem. 相似文献
102.
In this paper, we introduce a higher-order Mond–Weir dual for a set-valued optimization problem by virtue of higher-order contingent derivatives and discuss their weak duality, strong duality and converse duality properties. 相似文献
103.
A simple scheme, with special terms and symbols useful in categorizing various nanostructures, is introduced. Using “n-D in/on m-D” composite nanomaterials where n,m ≤ 2 as examples, we illustrate how these terms and symbols can be used to represent various hetero nanostructures. This simple
nomenclature system also allows a systematization of a wide variety of multi-dimensional nanocomposite heterostructures. 相似文献
104.
105.
In this paper, we consider convergence properties of a class of penalization methods for a general vector optimization problem with cone constraints in infinite dimensional spaces. Under certain assumptions, we show that any efficient point of the cone constrained vector optimization problem can be approached by a sequence of efficient points of the penalty problems. We also show, on the other hand, that any limit point of a sequence of approximate efficient solutions to the penalty problems is a weekly efficient solution of the original cone constrained vector optimization problem. Finally, when the constrained space is of finite dimension, we show that any limit point of a sequence of stationary points of the penalty problems is a KKT stationary point of the original cone constrained vector optimization problem if Mangasarian–Fromovitz constraint qualification holds at the limit point.This work is supported by the Postdoctoral Fellowship of Hong Kong Polytechnic University. 相似文献
106.
Chongyang Liu Ryan Loxton Kok Lay Teo 《Journal of Optimization Theory and Applications》2014,163(3):957-988
In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in time followed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm. 相似文献
107.
J Zhou P E D Love X Wang K L Teo Z Irani 《The Journal of the Operational Research Society》2013,64(8):1091-1105
Optimizing construction project scheduling has received a considerable amount of attention over the past 20 years. As a result, a plethora of methods and algorithms have been developed to address specific scenarios or problems. A review of the methods and algorithms that have been developed to examine the area of construction schedule optimization (CSO) is undertaken. The developed algorithms for solving the CSO problem can be classified into three methods: mathematical, heuristic and metaheuristic. The application of these methods to various scheduling problems is discussed and implications for future research are identified. 相似文献
108.
109.
Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z2-symmetric toric code, SO(2N)1 and SU(3)1 state as well as the S3-symmetric SO(8)1 state and a non-Abelian chiral state we call the “4-Potts” state. 相似文献
110.
In this paper, we consider the existence and the uniqueness of solutions of piecewise nonlinear systems. We will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems. 相似文献