Abstract
This study presents an algorithm for solving Optimal Control Problems(OCPs) with objective function of the Lagrange - type and multiple delayson both the state and control variables of the constraints; with bounds on thecontrol variable. The full discretization of the objective functional and the multipledelay constraints was carried out using the Simpson numerical scheme.The discrete recurrence relations generated from the discretization of both theobjective functional and constraints were used to develop the matrix operatorswhich satisfy the basic spectral properties The primal-dual residuals of the algorithmwere derived in order to ascertain the rate of convergence of the algorithm;which performs faster when relaxed with an accelerator variant in the sense ofNesterov. The direct numerical approach for handling the multi-delay controlproblem was observed to obtain an accurate result at a faster rate of convergencewhen over-relaxed with an accelerator variant. This research problemis limited to linear constraints and objective functional of the Lagrange-typeand can address real-life models with multiple delays as applicable to quadraticoptimization of Intensity Modulated Radiation Theory (IMRT) planning. Thenovelty of this research paper lies in the method of discretization and its adaptationto handle linearly and proximal bound constrained program formulatedfrom the multiple delay optimal control problems.
Published Version
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