Combination of an adaptive multilevel SQP method and a space-time adaptive PDAE solver for optimal control problems

Abstract

We present an adaptive multilevel generalized SQP method to solve PDAE-constrained optimization problems. It explicitly allows the use of independent integration schemes such that all involved systems can be solved highly efficient and as accurate as desired. We will couple the optimization with the state-of-the-art PDAE solver KARDOS and apply the new tool to a radiative heat transfer problem described by space-time dependent non-linear partial differential algebraic equations. Results are presented, compared and discussed.

Variational data assimilation for transient blood flow simulations: Cerebral aneurysms as an illustrative example

“…57,65 This leads to a large, nonlinear system that couples all spatial and temporal DOFs of the discretised Navier-Stokes and adjoint Navier-Stokes equations. Solving this system requires the development of specialised solvers but can in some cases lead to superior performance compared with reduced approach (see, for example, Clever et al 66 ) and is therefore an interesting avenue for future improvements. NN9279K and NN9316K.…”

Approximating the Solution of Optimal Control Problems by Fuzzy Systems

“…M) can be different for each fuzzy approximator. Also in (11) we considered the initial condition x(t 0 ) = x 0 . If we have other initial conditions, for example if x(t 0 ) is free, then we must have p(t 0 ) = 0 and thus we can define p F in (11) as:…”

“…Thus conditions (3) can be stated in the following form: with the initial and final conditions x(0) = 0 and x(1) = 0.5. Thus the corresponding fuzzy system (see (11)) solutions can be constructed as follows:…”

“…Garg et al [10] presented a unified framework for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR) and Legendre-Gauss-Lobatto (LGL) points. An adaptive multilevel generalized SQP (sequential quadratic programming) method was presented by authors of [11], to solve PDAE-constrained (partial differential algebraic equations) optimization problems. The notion of KT-invexity, from mathematical programming was extended to the classical optimal control problem by authors of [12].…”

Adaptive Symmetric Interior Penalty Galerkin Method for Boundary Control Problems

“…The function u d , called desired control, is a guideline for the control; see, e.g., [14,26]. Note that this formulation also allows for the special and most common case, u d = 0, i.e., there is no a priori information on the optimal control.…”