We consider the convex parametric quadratic programming problem when the end of the parametric interval is caused by a multiplicity of possibilities ("ties"). In such cases, there is no clear way for the proper active set to be determined for the parametric analysis to continue. In this thesis, we show that the proper active set may be determined in general by solving a certain non-parametric quadratic programming problem. We simplify the parametric quadratic programming problem with a parameter both in the linear part of the objective function and in the right-hand side of the constraints to a quadratic programming without a parameter. We break the analysis into three parts. We first study the parametric quadratic programming problem with a parameter only in the linear part of the objective function, and then a parameter only in the right-hand side of the constraints. Each of these special cases is transformed into a quadratic programming problem having no parameters. A similar approach is then applied to the parametric quadratic programming problem having a parameter both in the linear part of the objective function and in the right-hand side of the constraints.

No description available.

Thesis (Ph. D.)--University of Washington, 1986. / Vita. Bibliography: leaves [164]-168.

The purpose of this dissertation was to provide a review of the theory of Optimization, in particular quadratic programming, and the algorithms suitable for solving both convex and non-convex quadratic programming problems. Optimization problems arise in a wide variety of fields and many can be effectively modeled with linear equations. However, there are problems for which linear models are not sufficient thus creating a need for non-linear systems. This dissertation includes a literature study of the formal theory necessary for understanding optimization and an investigation of the algorithms available for solving a special class of the non-linear programming problem, namely the quadratic programming problem. It was not the intention of this dissertation to discuss all possible algorithms for solving the quadratic programming problem, therefore certain algorithms for convex and non-convex quadratic programming problems were selected for a detailed discussion in the dissertation. Some of the algorithms were selected arbitrarily, because limited information was available comparing the efficiency of the various algorithms. Algorithms available for solving general non-linear programming problems were also included and briefly discussed as they can be used to solve quadratic programming problems. A number of algorithms were then selected for evaluation, depending on the frequency of use in practice and the availability of software implementing these algorithms. The evaluation included a theoretical and quantitative comparison of the algorithms. The quantitative results were analyzed and discussed and it was shown that the results supported the theoretical comparison. It was also shown that it is difficult to conclude that one algorithm is better than another as the efficiency of an algorithm greatly depends on the size of the problem, the complexity of an algorithm and many other implementation issues. Optimization problems arise continuously in a wide range of fields and thus create the need for effective methods of solving them. This dissertation provides the fundamental theory necessary for the understanding of optimization problems, with particular reference to quadratic programming problems and the algorithms that solve such problems. Keywords: Quadratic Programming, Quadratic Programming Algorithms, Optimization, Non-linear Programming, Convex, Non-convex.

Liu Shubao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 90-98). / Abstracts in English and Chinese. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Time-Varying Quadratic Optimization --- p.1 / Chapter 1.2 --- Recurrent Neural Networks --- p.3 / Chapter 1.2.1 --- From Feedforward to Recurrent Networks --- p.3 / Chapter 1.2.2 --- Computational Power and Complexity --- p.6 / Chapter 1.2.3 --- Implementation Issues --- p.7 / Chapter 1.3 --- Thesis Organization --- p.9 / Chapter I --- Theory and Models --- p.11 / Chapter 2 --- Linearly Constrained QP --- p.13 / Chapter 2.1 --- Model Description --- p.14 / Chapter 2.2 --- Convergence Analysis --- p.17 / Chapter 3 --- Quadratically Constrained QP --- p.26 / Chapter 3.1 --- Problem Formulation --- p.26 / Chapter 3.2 --- Model Description --- p.27 / Chapter 3.2.1 --- Model 1 (Dual Model) --- p.28 / Chapter 3.2.2 --- Model 2 (Improved Dual Model) --- p.28 / Chapter II --- Engineering Applications --- p.29 / Chapter 4 --- KWTA Network Circuit Design --- p.31 / Chapter 4.1 --- Introduction --- p.31 / Chapter 4.2 --- Equivalent Reformulation --- p.32 / Chapter 4.3 --- KWTA Network Model --- p.36 / Chapter 4.4 --- Simulation Results --- p.40 / Chapter 4.5 --- Conclusions --- p.40 / Chapter 5 --- Dynamic Control of Manipulators --- p.43 / Chapter 5.1 --- Introduction --- p.43 / Chapter 5.2 --- Problem Formulation --- p.44 / Chapter 5.3 --- Simplified Dual Neural Network --- p.47 / Chapter 5.4 --- Simulation Results --- p.51 / Chapter 5.5 --- Concluding Remarks --- p.55 / Chapter 6 --- Robot Arm Obstacle Avoidance --- p.56 / Chapter 6.1 --- Introduction --- p.56 / Chapter 6.2 --- Obstacle Avoidance Scheme --- p.58 / Chapter 6.2.1 --- Equality Constrained Formulation --- p.58 / Chapter 6.2.2 --- Inequality Constrained Formulation --- p.60 / Chapter 6.3 --- Simplified Dual Neural Network Model --- p.64 / Chapter 6.3.1 --- Existing Approaches --- p.64 / Chapter 6.3.2 --- Model Derivation --- p.65 / Chapter 6.3.3 --- Convergence Analysis --- p.67 / Chapter 6.3.4 --- Model Comparision --- p.69 / Chapter 6.4 --- Simulation Results --- p.70 / Chapter 6.5 --- Concluding Remarks --- p.71 / Chapter 7 --- Multiuser Detection --- p.77 / Chapter 7.1 --- Introduction --- p.77 / Chapter 7.2 --- Problem Formulation --- p.78 / Chapter 7.3 --- Neural Network Architecture --- p.82 / Chapter 7.4 --- Simulation Results --- p.84 / Chapter 8 --- Conclusions and Future Works --- p.88 / Chapter 8.1 --- Concluding Remarks --- p.88 / Chapter 8.2 --- Future Prospects --- p.88 / Bibliography --- p.89

In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. / In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems. / The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. / Liu, Chunli. / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3764. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 140-153). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Clock mesh is widely used in microprocessor designs for achieving low clock skew and high process variation tolerance. Clock mesh optimization is a very diffcult problem to solve because it has a highly connected structure and requires accurate delay models which are computationally expensive. Existing methods on clock network optimization are either restricted to clock trees, which are easy to be separated into smaller problems, or naive heuristics based on crude delay models. A clock mesh sizing algorithm, which is aimed to minimize total mesh wire area with consideration of clock skew constraints, has been proposed in this research work. This algorithm is a systematic solution search through rigorous Sequential Quadratic Programming (SQP). The SQP is guided by an efficient adjoint sensitivity analysis which has near-SPICE(Simulation Program for Integrated Circuits Emphasis)-level accuracy and faster-than-SPICE speed. Experimental results on various benchmark circuits indicate that this algorithm leads to substantial wire area reduction while maintaining low clock skew in the clock mesh. The reduction in mesh area achieved is about 33%.

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Lee, Eva K.; Committee Member: Barnes, Earl; Committee Member: Hertel, Nolan E.; Committee Member: Johnson, Ellis; Committee Member: Monteiro, Renato D.C.

Proefschrift--Nederlandsche Economische Hoogeschool, Rotterdam. / "Stellingen": [4] p. inserted.

Proefschrift--Nederlandsche Economische Hoogeschool, Rotterdam. / "Stellingen": [4] p. inserted.