First- and second-order necessary conditions with respect to components for discrete optimal control problems

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are obtained on the fly

Prevalence, predictors, and outcomes of patient prosthesis mismatch in women undergoing TAVI for severe aortic stenosis: Insights from the WIN-TAVI registry

Objective: To evaluate the incidence, predictors and outcomes of female patients with patient-prosthesis mismatch (PPM) following transcatheter aortic valve intervention (TAVI) for severe aortic stenosis (AS). Background: Female AS TAVI recipients have a significantly lower mortality than surgical aortic valve replacement (SAVR) recipients, which could be attributed to the potentially lower PPM rates. TAVI has been associated with lower rates of PPM compared to SAVR. PPM in females post TAVI has not been investigated to date. Methods: The WIN-TAVI (Women's INternational Transcatheter Aortic Valve Implantation) registry i

Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics

Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries. This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids. The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li$_x$FePO$_4$.Comment: research account, 17 two-column pages, 12 figs, 78 refs - some typos corrected Accounts of Chemical Research (2013

First- and second-order necessary conditions with respect to components for discrete optimal control problems

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are obtained on the fly