Gao Jianjun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 75-76). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Solution Framework Using Dynamic Programming --- p.7 / Chapter 2.1 --- Difficulty of using dynamic programming --- p.8 / Chapter 2.2 --- Scalar-state problems --- p.12 / Chapter 2.3 --- Time-invariant system --- p.17 / Chapter 2.4 --- Illustrative example of a scalar-state problem --- p.21 / Chapter 3 --- Cardinality Constrained Quadratic Optimization --- p.26 / Chapter 3.1 --- Reformulation --- p.27 / Chapter 3.2 --- NP hardness --- p.31 / Chapter 3.3 --- Solving CCQP with an efficient branch and bound method --- p.34 / Chapter 3.3.1 --- Efficient branch and bound algorithm --- p.34 / Chapter 3.3.2 --- Geometrical interpretation of the proposed ranking order --- p.48 / Chapter 3.3.3 --- Additional algorithmic ideas for enhancing computational efficiency --- p.56 / Chapter 3.4 --- Numerical example and computational results --- p.60 / Chapter 4 --- Summary and Future Work --- p.73

Although cardinality constraints naturally arise in many applications, e.g., in portfolio selection problems of choosing small number of assets from a large pool of stocks or dynamic portfolio selection problems with limited trading dates within a given time horizon and in subset selection of the regression analysis, the state-of-the-art in cardinality constrained optimization has been stagnant up to this stage, largely due to the inherent combinatorial nature of such hard problems. We focus in this research on developing efficient and implementable solution algorithms for cardinality constrained optimization by investigating prominent structures and hidden properties of such problems. More specifically, we develop solution algorithms for four specific cardinality constrained optimization problems, including (i) the cardinality constrained linear-quadratic control problem, (ii) the optimal control problem of linear switched system with limited number of switching, (iii) the time cardinality constrained dynamic mean- variance portfolio selection problem, and (iv) cardinality constrained quadratic optimization problem. Taking advantages of a linear-quadratic structure of cardinality constrained optimization problems, we strive for analytical solutions when possible. More specifically, we derive an analytical solution for problem (iii) and obtain for both problems (i) and (ii) semi-analytical expressions of the solution governed by a family of Ricatti-like equations, which still suffer an exponentially growing complexity. To achieve high-performance of the solution algorithm, we devise algorithms of a branch and bound (BnB) type with various tight and computationally-cheap lower bounds achieved by identifying suitable SDP formulations and by exploiting geometric properties of the problem. We demonstrate efficiency of our proposed solution schemes evidenced from numerical experiments and present a firm step-forward in tackling this long-standing challenge of cardinality constrained optimization. / Gao, Jianjun. / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 134-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Hu San-qing. / "December 2001." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 181-192). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

University of Macau / Faculty of Science and Technology / Department of Mathematics

Thesis (M. Sc.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Dec. 30, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Process Control, Department of Chemical and Materials Engineering, University of Alberta." Includes bibliographical references.

Includes bibliographical references (p. 121-124).

Thesis (Ph. D.)--Ohio University, November, 1995. / Title from PDF t.p.

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 39-40). Also available on the World Wide Web.

Thesis (Ph.D.)--University of Wollongong, 2008. / Typescript. Includes bibliographical references: p. 227-238.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 145-153).