Thesis (M.S. in Operations Research)--Naval Postgraduate School, September 2009. / Thesis Advisor(s): Brown, Gerald G. "September 2009." Description based on title screen as viewed on November 5, 2009. Author(s) subject terms: Optimization, Mathematical Programming, Heuristic Algorithms, Network Flows, Anti-Submarine Warfare, Search and Detection, Game Theory. Includes bibliographical references (p. 53). Also available in print.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 138-151).

Thesis (M.S.)--University of Wisconsin--Madison, 1967. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.A.)--Kutztown University of Pennsylvania, 1995. / Source: Masters Abstracts International, Volume: 45-06, page: 3188. Abstract precedes thesis as [1] preliminary leaf. Typescript. Includes bibliographical references (leaves 30-33).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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.

Typescript (photocopy).

The practical implementation of optimal control systems in large industrial process applications has been limited by the high costs of the required computing facilities. With the recent advances in component fabrication and the resultant decrease in hardware costs, special purpose computers, utilizing virtually no software at all, can be constructed as economical alternatives to presently available general purpose computers for use in optimal process controllers. A design for one such special purpose machine, an automatic optimizer, is presented in this thesis. Tests conducted on a working optimizer constructed on the basis of the given design, demonstrate that it is suitably fast and powerful for use in process controllers. In addition, the optimizer is inexpensive enough to be used as part of an economical process controller. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

In this thesis, the problem considered is that of linear static optimization of a large system which is composed of a finite number of subsystems, each characterized by its own constraint matrix and objective function. The total system is itself constrained by resource availabilities and other factors, and its objective function is the mathematical linear sum of the objective function of the subsystems. The total system constraints couple together all the subsystems. The total system is first reformulated as a two-level problem by decoup1ing the total system constraints utilizing an arbitrary partition of the total system resources and other factors according to the number of subsystems. At the upper level we have a so-called central problem having as an objective function the sum of the optima of the subsystems achieved for any given partition and constrained by the total available resources and other factors which can be partitioned. At the lower level we have the subproblems which are small-dimension linear programming problems parameterized on the right-hand side of the part of the constraints which resulted from the decoup1ing of the total system constraints. The resources vector of each subproblem's set of constraints contains the system common resources allocated to it by the central problem. Different allocations of these resources to each subsystem create multiparametric optimization problems for which we have solution methods. The subsystem solutions become functions of the central system allocation policies. Therefore, the major concern for optimization of the whole system is the discovery of the optimum allocation policy. The method that we introduce finds the optimum allocation policy in a finite number of different allocation iterations. The major steps in the development are the discovery that the minimal (in case of multiple solutions) shadow prices of the subsystems are equal at optimality to the central system shadow prices, and that a coordination of the subsystems for the purpose of achieving optimality of the total system can be organized by utilizing the concave relationships governing the subsystem shadow prices versus the resources allocated to these subsystems. The method offers significant computational and conceptual advantages over present decomposition techniques, since it disposes with the solution of a central problem and the subproblems at each iteration and substitutes instead a simple coordination operation and subsystem parametric optimization at each iteration after the first, where a full solution of the subsystems takes place.

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