Dynamical systems: stability, symbolic dynamics and chaos

This paper presents a novel approach based on canonical dual theory to discuss global optimization and nonlinear optimal control problems. By introducing a differential flow on the dual feasible space, a set of complete solutions is given regardless of convexity or nonconvexity of the original problem. Meanwhile, applications to a class of linear quadratic optimal control problems are discussed. An analytical form of the optimal control is expressed.

Applications of a New Dual Approach in Global Optimization and Optimal Control Problem

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.

Modified ADMM algorithm for solving proximal bound formulation of multi-delay optimal control problem with bounded control

This paper presents a global optimization method for solving general nonlinear programming
problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a
differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained,
and criteria for global optimality and existence of solutions are given. Our theorems improve and
generalize recent known results in the canonical duality theory. Applications to a class of constrained
optimal control problems are discussed. Particularly, an analytical form of the optimal control is
expressed. Some examples are included to illustrate this new approach.

/pdf/complete-solutions-to-general-box-constrained-global-4tvakyepns.pdf

Complete Solutions to General Box-Constrained Global Optimization Problems

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Complete Solutions to General Box-Constrained Global Optimization Problems