A Bregman forward-backward linesearch algorithm for nonconvex composite optimization: superlinear convergence to nonisolated local minima

We introduce Bella, a locally superlinearly convergent Bregman forward backward splitting method for minimizing the sum of two nonconvex functions, one of which satisfying a relative smoothness condition and the other one possibly nonsmooth. A key tool of our methodology is the Bregman forward-backward envelope (BFBE), an exact and continuous penalty function with favorable first- and second-order properties, and enjoying a nonlinear error bound when the objective function satisfies a Lojasiewicz-type property. The proposed algorithm is of linesearch type over the BFBE along candidate update directions, and converges subsequentially to stationary points, globally under a KL condition, and owing to the given nonlinear error bound can attain superlinear convergence rates even when the limit point is a nonisolated minimum, provided the directions are suitably selected

Learning from and with the education movements in Greece and Brazil: Knowledge, action and alternatives

The insights shared in this paper are based on research conducted in Greece and Brazil It is centered around the exploration of activist knowledge as a distinct form of knowledge. In doing this, it discusses the role of reflection in acquiring critical consciousness as well as the unified and holistic character of activist knowledge. This unity entails the intertwining of action with reflection and action with theory. It shows how critique forms a key feature of activist knowledge and highlights some nuances, tensions and contradictions inherent in the knowledge production of this kind. The latter is shown to be underpinned by plural dialogical processes, which further challenge and enrich knowledge produced in social movements. The paper aims to feedback insights from theory into praxis and vice versa. To achieve its aims, it approaches learning as an ongoing part of the quest for meaning and the quest of meaning as an integral part of acting

Robust Linear Regression Analysis - A Greedy Approach

The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical (considered nowadays) methods, recently it has attracted more attention in the context of sparse modeling, where several notable contributions have been made. In the present manuscript, a new approach is considered in the framework of greedy algorithms. The noise is split into two components: a) the inlier bounded noise and b) the outliers, which are explicitly modeled by employing sparsity arguments. Based on this scheme, a novel efficient algorithm (Greedy Algorithm for Robust Denoising - GARD), is derived. GARD alternates between a least square optimization criterion and an Orthogonal Matching Pursuit (OMP) selection step that identifies the outliers. The case where only outliers are present has been studied separately, where bounds on the \textit{Restricted Isometry Property} guarantee that the recovery of the signal via GARD is exact. Moreover, theoretical results concerning convergence as well as the derivation of error bounds in the case of additional bounded noise are discussed. Finally, we provide extensive simulations, which demonstrate the comparative advantages of the new technique

A Simple and Efficient Algorithm for Nonlinear Model Predictive Control

We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of a quadratic program at every iteration and, consequently, inner iterative procedures. As a result, when the problem is ill-conditioned or the prediction horizon is large, each outer iteration becomes computationally very expensive. We propose a line-search algorithm that combines forward-backward iterations (FB) and Newton-type steps over the recently introduced forward-backward envelope (FBE), a continuous, real-valued, exact merit function for the original problem. The curvature information of Newton-type methods enables asymptotic superlinear rates under mild assumptions at the limit point, and the proposed algorithm is based on very simple operations: access to first-order information of the cost and dynamics and low-cost direct linear algebra. No inner iterative procedure nor Hessian evaluation is required, making our approach computationally simpler than SQP methods. The low-memory requirements and simple implementation make our method particularly suited for embedded NMPC applications

Pushover analysis for seismic assessment and design of structures

The earthquake resistant design of structures requires that structures should sustain, safely, any ground motions of an intensity that might occur during their construction or in their normal use. However ground motions are unique in the effects they have on structural responses. The most accurate analysis procedure for structures subjected to strong ground motions is the time-history analysis. This analysis involves the integration of the equations of motion of a multi-degree-of-freedom system, MDOF, in the time domain using a stepwise solution in order to represent the actual response of a structure. This method is time-consuming though for application in all practical purposes. The necessity for faster methods that would ensure a reliable structural assessment or design of structures subjected to seismic loading led to the pushover analysis. Pushover analysis is based on the assumption that structures oscillate predominantly in the first mode or in the lower modes of vibration during a seismic event. This leads to a reduction of the multi-degree-of-freedom, MDOF system, to an equivalent single-degreeof- freedom, ESDOF system, with properties predicted by a nonlinear static analysis of the MDOF system. The ESDOF system is then subsequently subjected to a nonlinear timehistory analysis or to a response spectrum analysis with constant-ductility spectra, or damped spectra. The seismic demands calculated for the ESDOF system are transformed through modal relationships to the seismic demands of the MDOF system. In this study the applicability of the pushover method as an alternative mean to general design and assessment is examined. Initially a series of SDOF systems is subjected to two different pushover methods and to nonlinear-time-history analyses. The results from this study show that pushover analysis is not able to capture the seismic demands imposed by far-field or near-fault ground motions, especially for short-period systems for which it can lead to significant errors in the estimation of the seismic demands. In the case of near-fault ground motions the results suggest that pushover analysis may underestimate the displacement demands for systems with periods lower than half the dominant pulse period of the ground motion and overestimate them for systems with periods equal or higher than half the dominant pulse period of the ground motion. Subsequently a two-degree-offreedom, 2-DOF, is studied in the same manner with specific intention to assess the accuracy of the different load patterns proposed in the literature. For this system pushover analysis performed similarly as in the SDOF study. Finally the method is applied on a four-storey reinforced concrete frame structure. For this study pushover analysis was not effective in capturing the seismic demands imposed by both a far-field and a near-fault ground motion. Overall pushover analysis can be unconservative in estimating seismic demands of structures and it may lead to unsafe design