A dissertation submitted to the Faculty of Arts, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Arts. / Real-life decision-making problems can often be modelled by mathematical programs (or optimization models). It is common for there to be uncertainty about the parameters of such optimization models. Usually, this uncertainty is ignored and a simplified deterministic program is obtained. Stochastic programs take account of this uncertainty by including a probabilistic description of the uncertain parameters in the model. Stochastic programs are therefore more appropriate or valuable than deterministic programs in many situations, and this is emphasized throughout the dissertation. The dissertation contains a development of the theory of stochastic programming, and a number of illustrative examples are formulated and solved. As a real-life application, a stochastic model for the unit commitment problem facing Eskom (one of the world's largest producers of electricity) is formulated and solved, and the solution is compared with that of the current strategy employed by Eskom. / AC 2018

Typescript, etc. / Digitized by Kansas Correctional Industries

Multistage stochastic programming is an important tool in medium to long term planning where there are uncertainties in the data. In this thesis, we consider a special case of multistage stochastic programming in which each subprogram is a convex quadratic program. The results are also applicable if the quadratic objectives are replaced by convex piecewise quadratic functions. Convex piecewise quadratic functions have important application in financial planning problems as they can be used as very flexible risk measures. The stochastic programming problems can be used as multi-period portfolio planning problems tailored to the need of individual investors. Using techniques from convex analysis and sensitivity analysis, we show that each subproblem of a multistage quadratic stochastic program is a polyhedral piecewise quadratic program with convex Lipschitz objective. The objective of any subproblem is differentiable with Lipschitz gradient if all its descendent problems have unique dual variables, which can be guaranteed if the linear independence constraint qualification is satisfied. Expression for arbitrary elements of the subdifferential and generalized Hessian at a point can be calculated for quadratic pieces that are active at the point. Generalized Newton methods with linesearch are proposed for solving multistage quadratic stochastic programs. The algorithms converge globally. If the piecewise quadratic objective is differentiable and strictly convex at the solution, then convergence is also finite. A generalized Newton algorithm is implemented in Matlab. Numerical experiments have been carried out to demonstrate its effectiveness. The algorithm is tested on random data with 3, 4 and 5 stages with a maximum of 315 scenarios. The algorithm has also been successfully applied to two sets of test data from a capacity expansion problem and a portfolio management problem. Various strategies have been implemented to improve the efficiency of the proposed algorithm. We experimented with trust region methods with different parameters, using an advanced solution from a smaller version of the original problem and sorting the stochastic right hand sides to encourage faster convergence. The numerical results show that the proposed generalized Newton method is a highly accurate and effective method for multistage quadratic stochastic programs. For problems with the same number of stages, solution times increase linearly with the number of scenarios.

Thesis (M.S.)--University of Kentucky, 2003. / Title from document title page (viewed June 21, 2004). Document formatted into pages; contains viii, 55 p. : ill. Includes abstract and vita. Includes bibliographical references (p. 52-54).

published_or_final_version / Computer Science / Master / Master of Philosophy

No description available.

No description available.

No description available.

No description available.

No description available.