Imbedding the Multiplier in a Discretized Optimal Control Problem With Real Coefficients Via the Penalty and Multiplier Methods
DOI : 10.3844/jmssp.2010.23.27
Journal of Mathematics and Statistics
Volume 6, Issue 1
Problem statement: Many earlier schemes, particularly the Function Space Algorithm (FSA) which sidetracks the knowledge of operator, for solving quadratic optimal control problems have been computationally involving and iteratively high. Approach: Though, some of these earlier schemes developed operators consisting of complicated integrals still very difficult to evaluate. Here, objectively, a new scheme, Discretized Continuous Algorithm (DCA), is proposed with developed associated operator consisting of a series of summation replacing the integrals of the earlier schemes, thus enhancing much more feasible results and lower iterations. Results: Methodologically, the new scheme uses the penalty-multiplier method to obtain an unconstrained formulation whose bilinear form expression leads to the construction of operator amenable to the Conjugate Gradient Method (CGM). Conclusion/Recommendations: An hypothetical example is considered and results, tabulated per cycle, are more feasible and less iterative than some of the existing methods.
© 2010 O. Olotu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.