By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are prov...By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are proved in generalized convex spaces without linear structure. These theorems improve and generalize a number of important results in recent literature.展开更多
Polar dielectrics are important optical materials enabling the subwavelength manipulation of light in infrared due to their capability to excite phonon polaritons.In practice,it is highly desired to actively modify th...Polar dielectrics are important optical materials enabling the subwavelength manipulation of light in infrared due to their capability to excite phonon polaritons.In practice,it is highly desired to actively modify these hyperbolic phonon polaritons（HPPs） to optimize or tune the response of the device.In this work,we investigate the plasmonic material,a monolayer graphene,and study its hybrid structure with three kinds of hyperbolic thin films grown on SiO_2 substrate.The inter-mode hybridization and their tunability have been thoroughly clarified from both the band dispersions and the mode patterns numerically calculated through a transfer matrix method.Our results show that these hybrid multilayer structures are of strong potentials for applications in plasmonic waveguides,modulators and detectors in infrared.展开更多
This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's ...This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.展开更多
In order to solve the so-called minimum period control problem for a class of abstract evolutionary systems, the authors study an infinite dimensional time optimal control problem with mixed type target set. To the l...In order to solve the so-called minimum period control problem for a class of abstract evolutionary systems, the authors study an infinite dimensional time optimal control problem with mixed type target set. To the latter problem complete results are established, which then are applied to the former to derive the desirable answer.展开更多
We analyze the classical penalty algorithm for nonlinear programming in Hilbert spaces and obtain global convergence results, as well as asymptotic superlinear convergence order. These convergence results generalize s...We analyze the classical penalty algorithm for nonlinear programming in Hilbert spaces and obtain global convergence results, as well as asymptotic superlinear convergence order. These convergence results generalize similar results obtained for finite-dimensional problems. Moreover, the nature of the algorithms allows us to solve the unconstrained subproblems in finite-dimensional spaces.展开更多
文摘By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are proved in generalized convex spaces without linear structure. These theorems improve and generalize a number of important results in recent literature.
基金Project supported by the National Natural Science Foundation of China(Grant No.61271085)the Natural Science Foundation of Zhejiang Province,China(Grant No.LR15F050001)
文摘Polar dielectrics are important optical materials enabling the subwavelength manipulation of light in infrared due to their capability to excite phonon polaritons.In practice,it is highly desired to actively modify these hyperbolic phonon polaritons（HPPs） to optimize or tune the response of the device.In this work,we investigate the plasmonic material,a monolayer graphene,and study its hybrid structure with three kinds of hyperbolic thin films grown on SiO_2 substrate.The inter-mode hybridization and their tunability have been thoroughly clarified from both the band dispersions and the mode patterns numerically calculated through a transfer matrix method.Our results show that these hybrid multilayer structures are of strong potentials for applications in plasmonic waveguides,modulators and detectors in infrared.
文摘This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.
文摘In order to solve the so-called minimum period control problem for a class of abstract evolutionary systems, the authors study an infinite dimensional time optimal control problem with mixed type target set. To the latter problem complete results are established, which then are applied to the former to derive the desirable answer.
文摘We analyze the classical penalty algorithm for nonlinear programming in Hilbert spaces and obtain global convergence results, as well as asymptotic superlinear convergence order. These convergence results generalize similar results obtained for finite-dimensional problems. Moreover, the nature of the algorithms allows us to solve the unconstrained subproblems in finite-dimensional spaces.
