Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some applications that slows its convergence. Restart schemes seek to improve the convergence of FGM algorithms by suppressing the oscillatory behaviour. Recently, a restart scheme for FGM has been proposed that provides linear convergence for non strongly convex optimization problems that satisfy a quadratic functional growth condition. However, the proposed algorithm requires prior knowledge of the optimal value of the objective function or of the quadratic functional growth parameter. In this paper we present a restart scheme for FISTA algorithm, with global linear convergence, for non strongly convex optimization problems that satisfy the quadratic growth condition without requiring the aforementioned values. We present some numerical simulations that suggest that the proposed approach outperforms other restart FISTA schemes.

In this paper we present an implementation of a low memory footprint Model Predictive Control (MPC) based controller in Programmable Logic Controllers (PLC). Automatic code generation of standardized IEC 61131-3 PLC programming languages is used to solve the MPC's optimization problem online. The implementation is designed for its application in a realistic industrial environment, including timing considerations and accounting for the possibility of the PLC not being exclusively dedicated to the MPC controller. We describe the controller architecture and algorithm, show the results of its memory footprint with regards to the problem dimensions and present the results of its implementation to control a hardware in the loop multivariable chemical plant.

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