Browsing by Author "Thrall, Robert M."
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Item Analytical studies of a class of two-person non-zero-sum games(1976) Batiz Solorzano, Sergio; Thrall, Robert M.In general, consideration of the non-cooperative case of a two-person non-zero-sum game leads to a more restricted set of feasible outcomes than the cooperative oase of the same game since correlated strategies are not permitted# An approach to describing such set of feasible outcomes for a class of games is given. Characterization seems plausible but there still are some open questions. The class of games of interest is one defined by a 2 by 2 bimatrix game having two pure strategy non-permutable equilibrium points, one for each player, and a third equilibrium point with the same features as the others given by the threat strategies.Item Benefit-cost analysis in rehabilitation programs(1980) Chan, Shou Alice; Thrall, Robert M.; Scott, David W.; Cardus, DavidThis thesis is concerned with an evaluation process for selection of rehabilitation research projects. An existing several-variable model is studied and extended. The parts of this model that relate to construction of a utility function are discussed in detail. A number of examples are given for illustration.Item Numerical experiments on transformation techniques for minimax problems of optimal control(1982) Kuo, Yan Min; Miele, Angelo; Bowen, Ray M.; Thrall, Robert M.A transformation technique is employed in order to convert mini max problems of optimal control into the Mayer-Bolza problem of the calculus of variations. The transformation requires the proper augmentation of the state vector x(t), the control vector u(t), and the parameter vector TT. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter in being optimized. The transformation technique is then employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. The algorithm considered in this thesis belongs to the class of sequential gradient-restoration algorithms. The sequential gradient restoration algorithm is made up of a sequence of two-phase cycles, each cycle consisting of a gradient phase and a restoration phase. The principal property of this algorithm is that it produces a sequence of feasible suboptimal solutions. Each feasible solution is characterized by a lower value of the minimax performance index than any previous feasible solution. To facilitate numerical implementation, the interval of integration is normalized to unit length. Four test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation technique and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the known analytical solutions. In particular, the converged values of the minimax performance index agree well with the known analytical values.Item On the Construction of Strong Complementarity Slackness for DEA Linear Programming Problems Using a Primal-Dual Interior-Point Method(1994-11) González-Lima, María D.; Tapia, Richard A.; Thrall, Robert M.A novel approach for solving the DEA linear programming problems using a primal-dual interior-point method is presented. The solution found by this method satisfies the Strong Complementarity Slackness Condition (SCSC) and maximizes the product of the positive components among all SCSC solutions. This first property is critical in the use of DEA and the second one contributes significantly to the reliability of the solution.Item Restoration algorithm for solving optimal control problems with nondifferential constraints and general boundary conditions(1981) Huang, G. T. C.; Miele, Angelo; Bayazitoglu, Yildiz; Thrall, Robert M.This thesis considers the numerical solution of the problem of minimizing a functional I, subject to differential constraints, non-differential constraints, and general boundary conditions. It consists of finding the state x(t), the control u(t), and the parameter pi, so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. First, a new version of the restoration algorithm is developed, in order to solve the following sub-problem: find a feasible solution, starting from a non-feasible solution. This task is accomplished in a cycle, composed of several restorative iterations. In each restorative iteration, variations of the state, the control, and the parameter are produced so as to achieve first-order constraint satisfaction, while minimizing the norm squared of the variations of the control and the parameter. Next, a transformation technique is employed. By proper augmentation of the state vector and the parameter vector, and by proper redefinition of the constraining relations, a transformed system is obtained. In this transformed system, the value of the functional I becomes a component of the augmented parameter. Then, the original minimization problem is replaced by the problem of finding the smallest value of the parameter I for which the transformed system admits a feasible solution. In this connection, ways and means are explored for approaching the minimum of the parameter I by cyclical application of the restoration algorithm. As a whole, the minimization algorithm is composed of a sequence of restorative cycles. Two consecutive elements of the sequence are such that the value of the parameter I at the end of any cycle is smaller than the value of the parameter I at the end of the previous cycle. The driving force which enables the restoration algorithm to continue is the lowering of the value of parameter I after a feasible solution has been obtained. This supplies the disturbance necessary for the restoration algorithm to continue. Depending on the strategy employed for the driving parameter and the strategy employed for the error in the feasibility equations, different versions of the minimization algorithm are developed: Algorithms A1, A2, A3 and Algorithms B1, B2, B3. These versions are tested through four numerical examples, and it is found that they perform in a satisfactory way. Thus, the numerical results show the feasibility as well as the convergence characteristics of the present algorithm.Item Some game-theoretic considerations in energy problems(1976) Edmonds, Hobart John; Thrall, Robert M.This thesis is concerned with two independent gaming formulations. The first deals with the grand strategy space for the United States in a global energy game. The individual elements of this space are cataloged, with subsequent discussion of possible payoffs and difficulties in choosing the strategy options. Detection games are a wide class of formulations which can include certain energy conflict scenarios, A detection game constructed by another author, written with a military scenario, is examined in detail. Minimax results are sought for the detection problem, and the partial failure to derive minimax strategies in the initial formulation discussed.