The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraint sets assigned to the agents. Based on the augmented Lagrange method, a distributed primal-dual algorithm with a projection operation included is proposed to solve the problem. It is shown that with appropriately chosen constant step size, the local estimates derived at all agents asymptotically reach a consensus at an optimal solution. In addition, the value of the cost function at the time-averaged estimate converges with rate O( 1 k ) to the optimal value for the unconstrained problem. By these properties the proposed primal-dual algorithm is distinguished from the existing algorithms for distributed constrained optimization. The theoretical analysis is justified by numerical simulations.

Rational design and development of new-generation photocatalysts with high hydrogen evolution activity is recognized as an effective strategy to settle energy crisis. To this regard, hybrid photocatalysts of Au quantum dots embedded in rimous cadmium sulfide nanospheres are synthesized by using a simple hydrothermal process followed by photoreduction. The rimous cadmium sulfide nanospheres with rough surface and irregular fissures greatly strengthen their adhesion and interaction with Au quantum dots, which effectively facilitates the separation, restrains the recombination, and accelerates the consumption of photoinduced electron-hole pairs. Impressively, the highest photocatalytic activity for hydrogen generation (601.2 μmol h g ) and organic pollutant degradation (100% degradation in 80 min) is obtained by adjusting the Au mass loading to achieve uniform distribution. This work paves new way to the exploitation of highly efficient metal/semiconductor hybrid photocatalysts for clean energy generation and environment restoration.

The Changning–Menglian orogenic belt (CMOB) in the southeastern Tibetan Plateau, is considered as the main suture zone marking the closure of the Palaeo‐Tethys Ocean between the Indochina and Sibumasu blocks. Here, we investigate the recently discovered retrograded eclogites from this suture zone in terms of their petrological, geochemical and geochronological features, with the aim of constraining the metamorphic evolution and protolith signature. Two types of metabasites are identified: retrograded eclogites and mafic schists. The igneous precursors of the retrograded eclogites exhibit rare earth element distribution patterns and trace element abundance similar to those of ocean island basalts, and are inferred to have been derived from a basaltic seamount in an intra‐oceanic tectonic setting. In contrast, the mafic schists show geochemical affinity to arc‐related volcanics with the enrichment of Rb, Th and U, and depletion of Nb, Ta, Zr, Hf and Ti, and their protoliths possibly formed at an active continental margin tectonic setting. Retrograded eclogites are characterized by peak metamorphic mineral assemblages of garnet, omphacite, white mica, lawsonite and rutile, and underwent five‐stage metamorphic evolution, including pre‐peak prograde stage (M1) at 18–19 kbar and 400–420°C, peak lawsonite‐eclogite facies (M2) at 24–26 kbar and 520–530°C, post‐peak epidote–eclogite facies decompression stage (M3) at 13–18 kbar and 530–560°C, subsequent amphibolite facies retrogressive stage (M4) at 8–10 kbar and 530–600°C, and late greenschist facies cooling stage (M5) at 5–8 kbar and 480–490°C. Laser ablation inductively coupled plasma mass spectrometry (LA–ICP–MS) U–Pb spot analyses of zircon show two distinct age groups. The magmatic zircon from both the retrograded eclogite and mafic schist yielded protolith ages of 451 ± 3 Ma, which is consistent with the ages of Early Palaeozoic ophiolitic complexes and ocean island sequences in the CMOB reported in previous studies. In contrast, metamorphic zircon from the retrograded eclogite samples yielded consistent Triassic metamorphic ages of 246 ± 2 and 245 ± 2 Ma, which can be interpreted as the timing of closure of the Palaeo‐Tethys Ocean. The compatible peak metamorphic mineral assemblages, P–T–t paths and metamorphic ages, as well as the similar protolith signatures for the eclogites in the CMOB and Longmu Co–Shuanghu suture (LCSS) suggest that the two belts formed part of a cold oceanic subduction system in the Triassic. The main suture zone of the Palaeo‐Tethyan domain extends at least 1,500 km in length from the CMOB to the LCSS in the Tibetan Plateau. The identification of lawsonite‐bearing retrograded eclogites in the CMOB provides important insights into the tectonic framework and complex geological evolution of the Palaeo‐Tethys.