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41 
SystemLevel Algorithm Design for Radionavigation using UWB WaveformsIltis, Ronald A. 10 1900 (has links)
A radiolocation/navigation system is considered in which mobile nodes use ultrawideband (UWB) radios to obtain internode ranges via roundtrip travel time (RTT). Each node is also assumed to contain an inertial measurement unit (IMU) which generates 2D position estimates subject to Gaussian drift and additive noise errors. The key problem in such a system is obtaining 2 or 3D position estimates from the nonlinear UWB range measurements and fusing the resulting UWB and IMU estimates. The system presented uses a Steepest Descent Random Start (SDRS) algorithm to solve the nonlinear positioning problem. It is shown that SDRS is a stable algorithim under a realistic communications reciprocity assumption. The SDRS estimates are then treated as measurements by the navigation Kalman filter. The navigation filter also processes separate IMUderived position estimates to update node position/velocity. Simulation results for an urban corridor are given showing < 6 m. rms position errors.

42 
High performance continuous/discrete global optimization methods. / CUHK electronic theses & dissertations collection / Digital dissertation consortiumJanuary 2003 (has links)
Ng, Chi Kong. / "May 2003." / Thesis (Ph.D.)Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 175187). / 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 Company, [200] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

43 
Surrogate dual search in nonlinear integer programming.January 2009 (has links)
Wang, Chongyu. / Thesis (M.Phil.)Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 7478). / Abstract also in Chinese. / Abstract  p.1 / Abstract in Chinese  p.3 / Acknowledgement  p.4 / Contents  p.5 / List of Tables  p.7 / List of Figures  p.8 / Chapter 1.  Introduction  p.9 / Chapter 2.  Conventional Dynamic Programming  p.15 / Chapter 2.1.  Principle of optimality and decomposition  p.15 / Chapter 2.2.  Backward dynamic programming  p.17 / Chapter 2.3.  Forward dynamic programming  p.20 / Chapter 2.4.  Curse of dimensionality  p.23 / Chapter 3.  Surrogate Constraint Formulation  p.26 / Chapter 3.1.  Surrogate constraint formulation  p.26 / Chapter 3.2.  Singly constrained dynamic programming  p.28 / Chapter 3.3.  Surrogate dual search  p.29 / Chapter 4.  Distance Confined Path Algorithm  p.34 / Chapter 4.1.  Yen´ةs algorithm for the kth shortest path problem  p.35 / Chapter 4.2.  Application of Yen´ةs method to integer programming  p.36 / Chapter 4.3.  Distance confined path problem  p.42 / Chapter 4.4.  Application of distance confined path formulation to integer programming  p.50 / Chapter 5.  Convergent Surrogate Dual Search  p.59 / Chapter 5.1.  Algorithm for convergent surrogate dual search  p.62 / Chapter 5.2.  "Solution schemes for (Pμ{αk,αβ)) and f(x) = αk"  p.63 / Chapter 5.3.  Computational Results and Analysis  p.68 / Chapter 6.  Conclusions  p.72 / Bibliography  p.74

44 
General solution methods for mixed integer quadratic programming and derivative free mixed integer nonlinear programming problemsNewby, Eric 29 July 2013 (has links)
A dissertation submitted to the Faculty of Science School of Computational and Applied Mathematics, University of the Witwatersrand,
Johannesburg. April 27, 2013. / In a number of situations the derivative of the objective function of an optimization
problem is not available. This thesis presents a novel algorithm
for solving mixed integer programs when this is the case. The algorithm
is the first developed for problems of this type which uses a trust region
methodology. Three implementations of the algorithm are developed and
deterministic proofs of convergence to local minima are provided for two of
the implementations.
In the development of the algorithm several other contributions are made.
The derivative free algorithm requires the solution of several mixed integer
quadratic programming subproblems and novel methods for solving nonconvex
instances of these problems are developed in this thesis. Additionally,
it is shown that the current definitions of local minima for mixed integer programs
are deficient and a rigorous approach to developing possible definitions
is proposed. Using this approach we propose a new definition which improves
on those currently used in the literature.
Other components of this thesis are an overview of derivative based mixed
integer nonlinear programming, extensive reviews of mixed integer quadratic
programming and deterministic derivative free optimization and extensive
computational results illustrating the effectiveness of the contributions mentioned
in the previous paragraphs.

45 
Trajectorybased methods for solving nonlinear and mixed integer nonlinear programming problemsOliphant, TerryLeigh January 2016 (has links)
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015. / I would like to acknowledge a number of people who contributed towards the completion of
this thesis. Firstly, I thank my supervisor Professor Montaz Ali for his patience, enthusiasm,
guidance and teachings. The skills I have acquired during this process have infiltrated every
aspect of my life. I remain forever grateful. Secondly, I would like to say a special thank
you to Professor Jan Snyman for his assistance, which contributed immensely towards this
thesis. I would also like to thank Professor Dominque Orban for his willingness to assist me
for countless hours with the installation of CUTEr, as well as Professor Jose Mario Martinez
for his email correspondence. A heartfelt thanks goes out to my family and friends at large,
for their prayers, support and faith in me when I had little faith in myself. Thank you also to
my colleagues who kept me sane and motivated, as well as all the support staff who played a
pivotal roll in this process. Above all, I would like to thank God, without whom none of this
would have been possible.

46 
Global Optimization of Nonconvex Factorable Programs with Applications to Engineering Design ProblemsWang, Hongjie 12 June 1998 (has links)
The primary objective of this thesis is to develop and implement a global optimization algorithm to solve a class of nonconvex programming problems, and to test it using a collection of engineering design problem applications.The class of problems we consider involves the optimization of a general nonconvex factorable objective function over a feasible region that is restricted by a set of constraints, each of which is defined in terms of nonconvex factorable functions. Such problems find widespread applications in production planning, location and allocation, chemical process design and control, VLSI chip design, and numerous engineering design problems. This thesis offers a first comprehensive methodological development and implementation for determining a global optimal solution to such factorable programming problems. To solve this class of problems, we propose a branchandbound approach based on linear programming (LP) relaxations generated through various approximation schemes that utilize, for example, the MeanValue Theorem and Chebyshev interpolation polynomials, coordinated with a {em ReformulationLinearization Technique} (RLT). The initial stage of the lower bounding step generates a tight, nonconvex polynomial programming relaxation for the given problem. Subsequently, an LP relaxation is constructed for the resulting polynomial program via a suitable RLT procedure. The underlying motivation for these two steps is to generate a tight outer approximation of the convex envelope of the objective function over the convex hull of the feasible region. The bounding step is thenintegrated into a general branchandbound framework. The construction of the bounding polynomials and the node partitioning schemes are specially designed so that the gaps resulting from these two levels of approximations approach zero in the limit, thereby ensuring convergence to a global optimum. Various implementation issues regarding the formulation of such tight bounding problems using both polynomial approximations and RLT constructs are discussed. Different practical strategies and guidelines relating to the design of the algorithm are presented within a general theoretical framework so that users can customize a suitable approach that takes advantage of any inherent special structures that their problems might possess. The algorithm is implemented in C++, an objectoriented programming language. The class modules developed for the software perform various functions that are useful not only for the proposed algorithm, but that can be readily extended and incorporated into other RLT based applications as well. Computational results are reported on a set of fifteen engineering process control and design test problems from various sources in the literature. It is shown that, for all the test problems, a very competitive computational performance is obtained. In most cases, the LP solution obtained for the initial node itself provides a very tight lower bound. Furthermore, for nine of these fifteen problems, the application of a local search heuristic based on initializing the nonlinear programming solver MINOS at the node zero LP solution produced the actual global optimum. Moreover, in finding a global optimum, our algorithm discovered better solutions than the ones previously reported in the literature for two of these test instances. / Master of Science

47 
Location of stable and unstable equilibrium configurations using a model trust region quasiNewton method and tunnellingKwok, Heeyuen Herbert January 1983 (has links)
A hybrid method consists of a quasiNewton method and a homotopy method for locating multiple equilibrium configurations has been proposed recently. The hybrid method combined the efficiency of a quasiNewton method capable of locating stable and unstable equilibrium solutions with a robust homotopy method capable of tracking equilibrium paths with turning points and exploiting sparsity of the Jacobian matrix at the same time. A quasiNewton method in conjunction with a deflation technique is proposed here as an alternative to the hybrid method. The proposed method not only exploits sparsity and symmetry, but also represents an improvement in efficiency. Limit points and nearby equilibrium solutions, either stable or unstable, can be accurately located with the use of a modified pseudoinverse based on the singular value decomposition. This pseudoinverse modification destroys the Jacobian matrix sparsity, but is invoked only rarely (at limit arid bifurcation points where the Jacobian matrix is singular). / M.S.

48 
QuasiNewton algorithms for large scale nonlinear systemsVandenBrink, Dennis Jay January 1983 (has links)
In this work, an evaluation of a number of quasiNewton algorithms and strategies for sparse, symmetric Hessian matrices was performed. It was shown how these quasiNewton algorithms could be applied to the unconstrained minimization of a nonlinear function as well as a nonlinear least squares approach to solving a system of nonlinear equations. The best of these algorithms were evaluated for a problem with a fairly large number of degrees of freedom with a large load increment. From this study it is concluded that the proposed quasiNewton method with the double dogleg strategy and an automatic control on Hessian evaluations is the best algorithm for all of the problems considered in this investigation. The algorithm had no difficulty converging to solutions regardless of the size of the model and regardless of the size of the load or time step. The advantage of being able to take large load or time steps may lie in those problems which involve the location of critical points (limit or bifurcation points) of structures with minimal computational effort. All the algorithms which utilized the double dogleg strategy were consistently better able to converge to the solution  a clear validation of the globally convergent property of the double dogleg strategy. Finally, the usefulness of the double dogleg strategy in solving a system of nonlinear equations via the nonlinear least squares approach and in locating multiple equilibrium configurations using deflation speaks for the versatility of the proposed algorithm.
In conclusion, the quasiNewton algorithm proposed in this dissertation is both robust and efficient for small as well as large scale problems of matrices are exploited. Because sparsity and symmetry the algorithm does not place unreasonable demands on core storage requirements. Furthermore, using the deflation technique with tunneling the algorithm can be extremely useful for postbuckling response studies of structures involving many stable and unstable branches. / Ph. D.

49 
Nonlinear Programming Approaches for Efficient LargeScale Parameter Estimation with Applications in EpidemiologyWord, Daniel Paul 16 December 2013 (has links)
The development of infectious disease models remains important to provide scientists with tools to better understand disease dynamics and develop more effective control strategies. In this work we focus on the estimation of seasonally varying transmission parameters in infectious disease models from real measles case data. We formulate both discretetime and continuoustime models and discussed the benefits and shortcomings of both types of models. Additionally, this work demonstrates the flexibility inherent in largescale nonlinear programming techniques and the ability of these techniques to efficiently estimate transmission parameters even in very largescale problems. This computational efficiency and flexibility opens the door for investigating many alternative model formulations and encourages use of these techniques for estimation of larger, more complex models like those with agedependent dynamics, more complex compartment models, and spatially distributed data. How ever, the size of these problems can become excessively large even for these powerful estimation techniques, and parallel estimation strategies must be explored. Two parallel decomposition approaches are presented that exploited scenario based de composition and decomposition in time. These approaches show promise for certain types of estimation problems.

50 
OQGRG: a multistart algorithm for global solution of nonlinear and mixed integer programsUgray, Zsolt Gyula 28 August 2008 (has links)
Not available / text

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