Please use this identifier to cite or link to this item: `http://hdl.handle.net/2031/4523`

 Title: A new descent direction method for linearly constrained continuous optimization problems and its application in portfolio management Other Titles: Yi zhong xin de xia xiang fang fa ji zai tou zi zu he zhong de ying yong一種新的下降方法及在投資組合中的應用 Authors: Tong, Tak Chi (湯德芝) Department: Dept. of Manufacturing Engineering and Engineering Management Degree: Master of Philosophy Issue Date: 2004 Publisher: City University of Hong Kong Subjects: Mathematical optimizationPortfolio management -- Mathematical models Notes: CityU Call Number: HG4529.5.T66 2004Includes bibliographical references (leaves 43-46)Thesis (M.Phil.)--City University of Hong Kong, 2004v, 46 leaves ; 30 cm. Type: Thesis Abstract: The problem we consider in this thesis is a linearly constrained continuous optimization problem with lower and upper bounds on variables. To solve the problem, a logarithmic barrier function and a barrier parameter are introduced to incorporate the lower and upper bounds into the objective function and derive a barrier optimization problem. To solve the barrier problem, we have found a new descent direction, which is obtained by computing the analytical center of a linear programming problem. This descent direction has a nice feature that the lower and upper bounds are always satisfied automatically if the step length is a number between zero and one. Based on the new descent direction, a descent direction method is developed for approximating a solution of the linearly constrained optimization problem. For any given value of the barrier parameter, we prove that the method converges to a stationary point globally. A portfolio selection model with transaction cost is formulated in this thesis. The model is an extension of Harry Markowitz’s mean-variance portfolio selection model, which gives some numerical indications for investors to make their decisions. The literature shows that the transaction cost is a very important factor involved in every transaction. When the transaction cost is taken into consideration, the model becomes very complicated to solve. In this thesis, we have applied the new descent direction method to solve the portfolio selection model with transaction cost. Numerical experiments show that the method seems efficient. Keywords: Linear Constraints, Nonlinear Programming, Descent Direction, Interior-Point Method, Lagrange Multipliers, Portfolio Selection, Transaction Cost, Mean-Variance Analysis Online Catalog Link: http://lib.cityu.edu.hk/record=b1871667 Appears in Collections: MEEM - Master of Philosophy

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