Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

A Scalable Methylamine Gas Healing Strategy for High‐Efficiency Inorganic Perovskite Solar Cells

An easy and scalable methylamine (MA) gas healing method was realized for inorganic cesium‐based perovskite (CsPbX₃) layers by incorporating a certain amount of MAX (X=I or Br) initiators into the raw film. It was found that the excess MAX accelerated the absorption of the MA gas into the CsPbX₃ film and quickly turned it into a liquid intermediate phase. Through the healing process, a highly uniform and highly crystalline CsPbX₃ film with enhanced photovoltaic performance was obtained. Moreover, the chemical interactions between a series of halides and MA gas molecules were studied, and the results could offer guidance in further optimizations of the healing strategy.     

Linear End‐On Coordination Modes of CO2

The second case of linear end‐on and evidence for an unprecedented bridging end‐on coordination mode of CO₂ have been discovered for vanadium aryloxide complexes of the tetradentate ligand system (ONNO)^2? (ONNO=2,4‐Me₂‐2‐(OH) C₆H₂CH₂]₂N(CH₂)₂NMe₂). The reaction of divalent (ONNO)V^II (TMEDA) with CO₂ and under the appropriate reaction conditions affords the trivalent (ONNO)V^III(OH)(η¹‐CO₂) resulting from an intermediate CO₂ deoxygenation pathway followed by H‐atom abstraction from the aromatic solvent, and CO₂ fixation. In contrast, the reduction of trivalent (ONNO)V^IIICl(THF) with K, followed by exposure to CO₂ in ethereal solvent, afforded the dinuclear [(ONNO)V^II]₂ (μ_,η¹‐CO₂).