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• The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

#### First-order affine scaling continuous method for convex quadratic programming

Yue, Hongwei 24 January 2014 (has links)
We develop several continuous method models for convex quadratic programming (CQP) problems with di.erent types of constraints. The essence of the continuous method is to construct one ordinary di.erential equation (ODE) system such that its limiting equilibrium point corresponds to an optimal solution of the underlying optimization problem. All our continuous method models share the main feature of the interior point methods, i.e., starting from any interior point, all the solution trajectories remain in the interior of the feasible regions. First, we present an a.ne scaling continuous method model for nonnegativity constrained CQP. Under the boundedness assumption of the optimal set, a thorough study on the properties of the ordinary di.erential equation is provided, strong con­vergence of the continuous trajectory of the ODE system is proved. Following the features of this ODE system, a new ODE system for solving box constrained CQP is also presented. Without projection, the whole trajectory will stay inside the box region, and it will converge to an optimal solution. Preliminary simulation results illustrate that our continuous method models are very encouraging in obtaining the optimal solutions of the underlying optimization problems. For CQP in the standard form, the convergence of the iterative .rst-order a.ne scaling algorithm is still open. Under boundedness assumption of the optimal set and nondegeneracy assumption of the constrained region, we discuss the properties of the ODE system induced by the .rst-order a.ne scaling direction. The strong convergence of the continuous trajectory of the ODE system is also proved. Finally, a simple iterative scheme induced from our ODE is presented for find­ing an optimal solution of nonnegativity constrained CQP. The numerical results illustrate the good performance of our continuous method model with this iterative scheme. Keywords: ODE; Continuous method; Quadratic programming; Interior point method; A.ne scaling.
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23

#### Continuous-time recurrent neural networks for quadratic programming: theory and engineering applications.

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
24

#### A structured reduced sequential quadratic programming and its application to a shape design problem

Kang, Kyehong 07 June 2006 (has links)
The objective of this work is to solve a model one dimensional duct design problem using a particular optimization method. The design problem is formulated as an equality constrained optimization, called All at once method, so that the analysis problem is not solved until the optimal design is reached. Furthermore, the block structure in the Jacobian of the linearized constraints is exploited by decomposing the variables into the design and flow parts. To achieve this, Sequential quadratic programming with BFGS update for the reduced Hessian of the Lagrangian function is used with Variable reduction method which preserves the structure of the Jacobian in representing the null space basis matrix. By updating the reduced Hessians only of which the dimension is the number of design variables, the storage requirement for Hessians is reduced by a large amount. In addition, the flow part of the Jacobian can be computed analytically. The algorithm with a line search globalization is described. A global and local analysis is provided with a modification of the paper by Byrd and Nocedal [Mathematical Programming 49(1991) pp 285-323] in which they analyzed the similar algorithm with the Orthogonal factorization method which assumes the orthogonality of the null space basis matrix. Numerical results are obtained and compared favorably with results from the Black box method - unconstrained optimization formulation. / Ph. D.
25

#### Polynomial and indefinite quadratic programming problems: algorithms and applications

Tuncbilek, Cihan H. 03 August 2007 (has links)
This dissertation is concerned with the global optimization of polynomial programming problems, and a detailed treatment of its particular special case, the indefinite quadratic programming problem. Polynomial programming problems are generally nonconvex, involving the optimization of a polynomial objective function over a compact feasible region defined in terms of polynomial constraints. These problems arise in a variety of applications in the context of engineering design and chemical process design situations. Despite the wide applicability of these classes of problems, there is a significant gap between the theory and practice in this field, principally due to the challenge faced in solving these rather difficult problems. The purpose of this dissertation is to introduce new solution strategies that assist in closing this gap. For solving polynomial programming problems, we present a branch and bound algorithm that uses a Reformulation Linearization Technique (RLT) to generate tight linear programming relaxations. This bounding scheme involves an automatic reformulation of the problem via the addition of certain nonlinear implied constraints that are generated by using the products of the simple bounding restrictions and, optionally, products involving the structural constraints. Subsequently, in a linearization phase, each distinct nonlinear term in the resulting problem is replaced by a new variable to obtain a linear program. The underlying purpose of this procedure is to closely approximate the convex envelope of the objective function over the convex hull of the feasible region. Various implementation issues regarding the derivation of such a bounding problem using the RLT, and the dominance of such bounds over existing alternative schemes, are investigated, both the- theoretically and computationally. The principal thrust of the proposed method is to construct a tight linear programming relaxation of the problem via an appropriate RLT procedure, and to use this in concert with a suitable partitioning strategy, in order to derive a practically effective algorithm that is theoretically guaranteed to be globally convergent. To address various implementation issues, empirical experiments are conducted using several test problems from the literature, many motivated by the aforementioned practical applications. Our results on solving several such practical engineering design problems demonstrate the viability of the proposed approach. This approach is also specialized and further enhanced for the particular class of indefinite (and concave) quadratic programming problems. These problems are important in their own right, and arise in many applications such as in modelling economies of scale in a cost structure, in location-allocation problems, several production planning and risk management problems, and in various other mathematical models such as the maximum clique problem and the jointly constrained bilinear programming problem. The proposed algorithm is more than just a specialization of the polynomial programming approach; it involves new, nontrivial extensions that exploit the particular special structure of the problem, along with many additional supporting features that improve the computational efficiency of the procedure. Certain types of nonlinearities are also retained and handled implicitly within the bounding problem to obtain sharper bounds. Computational results are presented on a set of test problems from the literature to demonstrate the efficiency of the approach. (One of these test problems had not previously been solved to optimality.) It is shown that for many problems, including randomly generated problems having up to 50 variables, the initial relaxation itself produces an optimal or a near optimal solution. This is significant in that the proposed methodology affords an approach whereby such hard nonconvex problems can be practically solved via a single or a few higher dimensional linear programming problems. / Ph. D.
26

#### Projected Barzilai-Borwein Method with Infeasible Iterates for Nonnegative Image Deconvolution

Fraser, Kathleen 22 July 2011 (has links)
The Barzilai-Borwein (BB) method for unconstrained optimization has attracted attention for its "chaotic" behaviour and fast convergence on image deconvolution problems. However, images with large areas of darkness, such as those often found in astronomy or microscopy, have been shown to benefit from approaches which impose a nonnegativity constraint on the pixel values. We present a new adaptation of the BB method which enforces a nonnegativity constraint by projecting the solution onto the feasible set, but allows for infeasible iterates between projections. We show that this approach results in faster convergence than the basic Projected Barzilai-Borwein (PBB) method, while achieving better quality images than the unconstrained BB method. We find that the new method also performs comparably to the Gradient Projection-Conjugate Gradient (GPCG) method, and in most test cases achieves a lower restoration error, despite being a much simpler algorithm.
27

#### Aggregation in large scale quadratic programming

Foster, David Martin 08 1900 (has links)
No description available.
28

#### ESSAYS ON FRESH VEGETABLE PRODUCTION AND MARKETING PRACTICES

Vassalos, Michael 01 January 2013 (has links)
Commercial fresh vegetable production is one of the most rewarding and risky farming activities. The price and yield variations throughout the production year, the special characteristics of fresh vegetable produce (i.e. perishability), and the changing consumer demands are some of the factors contributing to the increased uncertainty faced by vegetable producers. This dissertation combined mathematical programming and econometric techniques to: 1) investigate the optimal production and marketing practices under different price distribution information scenarios, risk aversion levels and marketing outlets and 2) examine growers’ preferences as well the effect of risk aversion levels and growers’ risk perception on the choice of marketing contracts. Specifically, the following three modeling approaches were adopted in order to achieve the dissertation objectives: 1) quadratic programming under a mean-variance framework, 2) discrete choice experiments and 3) a combination of quadratic and integer programming embodied in a meanvariance framework. The findings indicate that optimal production practices and the resulting net returns are substantially influenced not only by the choice of marketing channel but also by growers’ risk aversion levels as well as price knowledge. Furthermore, regarding the choice of marketing contracts, the results highlight the existence of heterogeneity in preferences and illustrate the importance of certification cost, in line with the previous literature. Lastly, the findings indicate that risk aversion and risk preferences do not play a significant role in the choice of contractual agreements by farmers.
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