An all-at-once approach for the optimal control of the unsteady Burgers equation

We apply an all-at-once method for the optimal control of the unsteady Burgers equation. The nonlinear Burgers equation is discretized in time using the semi-implicit discretization and the resulting first order optimality conditions are solved iteratively by Newton's method. The discretize then optimize approach is used, because it leads to a symmetric indefinite saddle point problem. Numerical results for the distributed unconstrained and control constrained problems illustrate the performance of the all-at-once approach with semi-implicit time discretization

Brezzi-Pitkaranta stabilization and a priori error analysis for the Stokes Control

In this study, we consider a Brezzi-Pitkaranta stabilization scheme for the optimal control problem governed by stationary Stokes equation, using a P1-P1 interpolation for velocity and pressure. We express the stabilization as extra terms added to the discrete variational form of the problem.  We first prove the stability of the finite element discretization of the problem. Then, we derive a priori error bounds for each variable and present a numerical example to show the effectiveness of the stabilization clearly

Optimal boundary control of the unsteady Burgers equation with simultaneous space-time discretization

The optimality system for boundary controlled unsteady Burgers equation is transformed after linearization into a biharmonic equation in the space-time domain. It is then discretized in space and time simultaneously, so that standard finite element software can be easily implemented. Numerical experiments with and without control constraint problems confirm the applicability of this approach. Copyright (C) 2013 John Wiley & Sons, Ltd

Solving optimal control problems for the unsteady Burgers equation in COMSOL Multiphysics

The optimal control of unsteady Burgers equation without constraints and with control constraints are solved using the high-level modelling and simulation package COMSOL Multiphysics. Using the first-order optimality conditions, projection and semi-smooth Newton methods are applied for solving the optimality system. The optimality system is solved numerically using the classical iterative approach by integrating the state equation forward in time and the adjoint equation backward in time using the gradient method and considering the optimality system in the space-time cylinder as an elliptic equation and solving it adaptively. The equivalence of the optimality system to the elliptic partial differential equation (PDE) is shown by transforming the Burgers equation by the Cole-Hopf transformation to a linear diffusion type equation. Numerical results obtained with adaptive and nonadaptive elliptic solvers of COMSOL Multiphysics are presented both for the unconstrained and the control constrained case

Variational multiscale method for the optimal control problems of convection-diffusion-reaction equations

In this paper, we analyze a projection-based variational multiscale (VMS) method for the optimal control problems governed by the convection diffusion reaction equations. We derive the first-order optimality conditions by the optimize-then-discretize method. After expressing the discrete optimal control problem, we obtain the stability properties of state and adjoint variables. We also prove that the error in each variable is optimal. Through numerical examples, we show the efficiency of the stabilization for the solutions of the control, state, and adjoint variables

Minimal truncation error constants for Runge-Kutta method for stochastic optimal control problems

In this work, we obtain strong order-1 conditions with minimal truncation error constants of Runge–Kutta method for the optimal control of stochastic differential equations (SDEs). We match Stratonovich–Taylor expansion of the exact solution with Stratonovich–Taylor expansion of our approximation method that is defined by the Runge–Kutta scheme, term by term, in order to get the strong order-1 conditions. By a conclusion and an outlook to future research, the paper ends

A discrete optimality system for an optimal harvesting problem

In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge-Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications

Turkish League Against Rheumatism (TLAR) Recommendations for the Pharmacological Management of Rheumatoid Arthritis: 2018 Update Under Guidance of Current Recommendations

Objectives: This study aims to report the assessment of the Turkish League Against Rheumatism (TLAR) expert panel on the compliance and adaptation of the European League Against Rheumatism (EULAR) 2016 recommendations for the management of rheumatoid arthritis (RA) in Turkey. Patients and methods: The EULAR 2016 recommendations for the treatment of RA were voted by 27 specialists experienced in this field with regard to participation rate for each recommendation and significance of items. Afterwards, each recommendation was brought forward for discussion and any alteration gaining 70% approval was accepted. Also, Turkish version of each item was rearranged. Last version of the recommendations was then revoted to determine the level of agreement. Levels of agreement of the two voting rounds were compared with Wilcoxon signed-rank test. In case of significant difference, the item with higher level of agreement was accepted. In case of no difference, the changed item was selected.Results: Four overarching principles and 12 recommendations were assessed among which three overarching principles and one recommendation were changed. The changed overarching principles emphasized the importance of physical medicine and rehabilitation specialists as well as rheumatologists for the care of RA patients in Turkey. An alteration was made in the eighth recommendation on treatment of active RA patients with unfavorable prognostic indicators after failure of three conventional disease modifying anti-rheumatic drugs. Remaining principles were accepted as the same although some alterations were suggested but could not find adequate support to reach significance. Conclusion: Expert opinion of the TLAR for the treatment of RA was composed for practices in Turkish rheumatology and/or physical medicine and rehabilitation clinics