http://hdl.handle.net/10397/10 Search the Channel search http://158.132.160.63:8080/jspui/simple-search http://hdl.handle.net/10397/1033 Title: Semi-infinite programming and semi-definite optimization problems<br/><br/>Authors: Li, Shengjie<br/><br/>Abstract: The purpose of this thesis is to study combined semi-infinite and semi-definite programming problems (SISDP), generalized semi-infinite programming problenls (GSIP) and optimization problems with max-min constraints.; For (SISDP), we derive uniform dualities and zero duality gap properties between the problem (SISDP) and its Lagrangian-type dual problem. We first derive necessary and sufficient conditions for uniform dualities of both the homogeneous (SISDP) problem and the nonhomogeneous (SISDP) problem. Under a generalized canonical closedness condition, we establish uniform duality properties for (SISDP) problem. Moreover, we show that a zero duality gap exists between the problem(SISDP) and its dual problem if Slater's constraint qualification holds.; We prove the closedness property of the feasible set mapping for the parametric problem of (SISDP). We obtain a sufficient condition for the upper and lower semi-continuity of the value function of the parametric problem of (SISDP), We also investigate the lower semicontinuity of the value function of the dual parametric problem. On the Other hand, by assuming the continuity of the value function, we investigate the closedness, uniform compactness and upper semicontinuity of the solution set mapping for the parametric problem of (SISDP). We also show that the solution set mapping for its dual parametric problem is uniformly compact. Next, we develop two discretization algorithms, each with an adaptive scheme, for solving(SISDP) problem. We obtain the convergence results of both the algorithms. Finally, we apply these discretization algorithms to solve semi-infinite quadratically constrained quadratic programming, semi-infinite eigenvalue, the continuous-time envelope-constrained filtering and robust envelope-constraind filtering problems. The numerical results obtained illustrate the effectiveness and efficiency of the proposed methods.; For (GSIP), an auxiliary optimization problem is introduced. The relationship between local (respectively, global) optimal solutions of the problem (GSIP) and local (respectively global) optimal solution of the auxiliary optimization problem is obtained. By using the idea of the pattern search method, an algorithm is derived for solving the problem (GSIP). Under the convexity conditions of the objective function and the constraint set, we prove that the sequence generated by our algorithm is convergent with its limiting point satisfying a Fritz-John optimality condition. Numerical results obtained show that the algorithm is efficient.; An optimization problem with maximin constraints is considered. It is known that the optimization problem is equivalent to a standard nonlinear optimization problem in the sense that a local minimizer of one problem will give rise to a local minimizer of the other problem. We show that equivalent relationship between the two optimization problems is valid under weaker condition. Then, we develop a descent algorithm for solving the optimization problem with maximin constraints. Under the convexity conditions of the objective function and the constraint functions, we prove that the sequence generated by our algorithm is finite and the solution obtained when our algorithm stops is a local optimal solution. Numerical results are given to illustrate the effectiveness of the proposed algorithm.<br/><br/>Description: vii, 157 leaves : ill. ; 30 cm.; PolyU Library Call No.: [THS] LG51 .H577P AMA 2003 Li http://hdl.handle.net/10397/508 Title: Quantum entanglement of excitons in coupled quantum dots<br/><br/>Authors: Zhang, Ping; Chan, Cheong-ki; Xue, Qi-Kun; Zhao, Xian-Geng<br/><br/>Abstract: Optically controlled exciton dynamics in coupled quantum dots is studied. We show that the maximally entangled Bell states and Greenberger-Horne-Zeilinger (GHZ) states can be robustly generated by manipulating the system parameters to be at the avoided crossings in the eigenenergy spectrum. The analysis of population transfer is systematically carried out by using a dressed-state picture. In addition to the quantum dot configuration that has been discussed by Quiroga and Johnson [Phys. Rev. Lett. 83, 2270 (1999)], we show that the GHZ states also may be produced in a ray of three quantum dots with a shorter generation time. http://hdl.handle.net/10397/982 Title: Generalized Newton-type methods and their applications<br/><br/>Authors: Ling, Chen<br/><br/>Abstract: The main purposes of this thesis are to solve the semi-infinite programming (SIP) problems, the option price interpolation problems and the L2 spectral estimation problems by using some generalized Newton methods.; Our proposed methods have the following three features:(1) At each iteration, only a system of linear equations needs to be solved;(2) These methods have Global convergence;(3) These methods are shown to be locally supperlinearly convergent.; We also present a smoothing implicit programming method to solve the generalized semi-infinite programming (GSIP) problem with uncertainty.; The main contributions of this thesis are as follows.; We introduce a class of integral functions which arises from many applications such as nonsmooth equation reformulations of the option price problems, the SIP problems and the L2 spectral estimation problems. We investigate the differentiability, semi-smoothness and smoothing approximation properties of this class of integral functions. This content is mainly based on the papers 1, 3 and 4 in Underlying Papers. We introduce four kinds of algorithms for solving SIP problems. First, we present a smoothing sequential quadratic programming (SQP) algorithm. At each iteration of this algorithm, we only need to solve a quadratic program which is always feasible and solvable. The global convergence of the smoothing SQP algorithm is established under some mild conditions. Further, we present a smoothing projected Newton-type algorithm and prove its global and local superlinear convergence property. However, the accumulation point of an iterative sequence generated by these algorithms above may not be a stationary point of the original SIP problem. So, we propose the third method, say, smoothing Newton-type algorithm. For this algorithm, we not only prove its global and local superlinear convergence under some mild conditions, but also show that any accumulation point of an iterative sequence generated by it is a stationary point of the original SIP problem. Finally, based on the smoothing projected Newton-type algorithm, we develop a truncated projected Newton-type algorithm which can solve large scale SIP problems with 2000 decision variables. The feasibility for all algorithms is ensured by an integral function. For all these algorithms, numerical experiments are also given. These contents are mainly based on the papers 3-6 in Underlying Papers.; We discuss a generalized semi-infinite programming problem with uncertainty. We propose a reformulation of the considered problem by using the first order optimality conditions of the second stage optimization problem and present a smoothing implicit programming method to solve the problem with finite discrete distribution. Global convergence results are obtained. This content is mainly based on the paper 2 in Underlying Papers.; For option price interpolation problem, Wang, Yin and Qi (2004) presented a generalized Newton method for solving it and established its superlinear convergence rate. We show that the proposed method has at least 4/3-order convergence rate, and then give conditions under which this method has 3/2 order and quadratic convergence rate. And finally, we give a damped version of the generalized Newton method and show that it is globally convergent and the convergence order is at least 4/3. This content is mainly based on the paper 1 in Underlying Papers.; A Newton method for solving power spectrum estimation problems is proposed in Chapter 7, and it is proved that the method is at least 1+1/2m-order convergent rate. We also produce a globalized Newton-type method for solving the problem, which has at least 1+1/2m-order convergence rate. This content is mainly based on the paper 7 in Underlying Papers.<br/><br/>Description: xi, 203 leaves : ill. ; 30 cm.; PolyU Library Call No.: [THS] LG51 .H577P AMA 2005 Ling http://hdl.handle.net/10397/509 Title: Effect of initial conditions on interaction between a boundary layer and a wall-mounted finite-length-cylinder wake<br/><br/>Authors: Wang, H. F.; Zhou, Yu; Chan, Cheong-ki; Lam, Ka-se<br/><br/>Abstract: The effects of initial conditions on interaction between a boundary layer over a flat plate and flow around a wall-mounted finite-length cylinder were experimentally investigated. A square cylinder with a characteristic width (d) of 20 mm and a length of H=5d was vertically mounted on a horizontal flat plate. Three different boundary layers were investigated, their momentum thickness being 0.07d, 0.13d, and 0.245d, respectively, measured at the cylinder axis in the absence of the cylinder. All the experiments were carried out in a closed-loop water tunnel at a Reynolds numbers of 11 500 based on d and the free-stream velocity U[sub ∞]. It is found that initial boundary layer conditions have a profound effect on the near wake, including the flow near the cylinder free end that is well beyond the boundary layer. With increasing boundary layer thickness, the base vortex is enhanced, inducing a stronger upwash flow from the cylinder base, which acts to weaken the downwash free-end shear layer and the tip vortex. Consequently, spanwise vortices gain strength near the free end but impair near the wall, causing the ratio of symmetrically to antisymmetrically arranged vortices to vary and subsequently the Reynolds stresses to increase significantly in magnitude near the free end but to decrease near the wall.