A geometric framework for nonconvex optimization duality using augmented lagrangian functions

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems. Using the primal function of a constrained optimization problem, we apply our results both in the analysis of duality schemes constructed using augmented Lagrangian functions, and in establishing necessary and sufficient conditions for the convergence of penalty methods.     

Distributed multi-agent optimization with state-dependent communication

We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents over a randomly varying network topology to update his information state. We assume a state-dependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents. We study a projected multi-agent subgradient algorithm under state-dependent communication. The state-dependence of the communication introduces significant challenges and couples the study of information exchange with the analysis of subgradient steps and projection errors. We first show that the multi-agent subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one. Under some assumptions on the stepsize sequence, we provide convergence rate bounds on a “disagreement metric” between the agent estimates. Our bounds are time-nonhomogeneous in the sense that they depend on the initial starting time. Despite this, we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization problem with probability one under different assumptions on the local constraint sets and the stepsize sequence.     

Order restricted randomized designs for control versus treatment comparison

We develop a method of randomizing units to treatments that relies on subjective judgement or on possible coarse modeling to produce restrictions on the randomization. The procedure thus fits within the general framework of ranked set sampling. However, instead of selecting a single unit from each set for full measurement, all units within a set are used. The units within a set are assigned to different treatments. Such an assignment translates the positive dependence among units within a set into a reduction in variation of contrasting features of the treatments. A test for treatment versus control comparison, with controlled familywise error rate, is developed along with the associated confidence intervals. The new procedure is shown to be superior to corresponding procedures based on completely randomized or ranked set sample designs. The superiority appears both in asymptotic relative efficiency and in power for finite sample sizes. Importantly, this test does not rely on perfect rankings; rather, the information in the data on the quality of rankings is exploited to maintain the level of the test when rankings are imperfect. The asymptotic relative efficiency of the test is not affected by estimation of the quality of rankings, and the finite sample performance is only mildly affected.     

Intersubband transitions in quantum wells under intense laser field

An intense laser field effect on the intersubband transitions in quantum wells is theoretically investigated within the framework of the effective-mass approximation. Results obtained show that intersubbband optical transitions and energy levels in quantum wells can be significantly modified and controlled by an intense laser field. PACS 71.55.Eq; 73.21.Fg; 78.67.De     

Out-of-plane dynamic stability analysis of curved beams subjected to uniformly distributed radial loading

In this study, out-of-plane stability analysis of tapered cross-sectioned thin curved beams under uniformly distributed radial loading is performed by using the finite-element method. Solutions referred to as Bolotin’s approach are analysed for dynamic stability, and the first unstable regions are examined. Out-of-plane vibration and out-of-plane buckling analyses are also studied. In addition, the results obtained in this study are compared with the published results of other researchers for the fundamental frequency and critical lateral buckling load. The effects of subtended angle, variations of cross-section, and dynamic load parameter on the stability regions are shown in graphics     

Synthesis of chiral acetoxy lactones via the Baeyer-Villiger oxidation of cyclic aromatic acetoxy ketones

The α-acetoxylation of indanones and tetralones by using Mn(OAc)₃ followed by the enzyme catalyzed kinetic resolution of acetoxy ketones furnished both of the enantiomers of α-acetoxy ketones in good chemical and optical yields. The Baeyer-Villiger oxidation of α-acetoxy ketones with m-CPBA, CF₃SO₃H, and CH₂Cl₂, at rt gives the corresponding lactones without racemization. The acetoxy ketone moiety migrates selectively in order to form lactones. The mild hydrolysis of lactones affords phenolic α-hydroxycarboxylic acid derivatives.     

High-Throughput Testing of Heterogeneous Catalyst Libraries Using Array Microreactors and Mass Spectrometry

Eighty isolated channels are present in the array microreactor system that was coupled to a quadrupole mass spectrometer for high-throughput testing of heterogeneous catalyst libraries. The system was used to monitor the activities, selectivities, and reaction kinetics of 66 ternary Pt/Pd/In catalysts for the dehydrogenation of cyclohexane to benzene over 24 h. It was possible to screen the entire 80-channel library in less than 10 minutes (see picture).     

Adsorption of Cu(II) ions from aqueous solution by hazelnut husk activated carbon prepared with potassium acetate

Hazelnut husk (HH), an agricultural waste, was converted to carbonaceous material by chemical activation using potassium acetate. The produced activated carbon (KAHHAC) was characterized by FTIR, SEM, N₂ adsorption–desorption experiments, CHN elemental analysis, and determination of moisture, ash, and point of zero charge. KAHHAC was used for the batch adsorption of Cu(II) ions from aqueous solutions. Optimum pH and contact time were found to be 5.0 and 240 minutes, respectively. The adsorption equilibrium data were described well by the Langmuir equation providing 105.3?mg?g^?1 Cu(II) adsorption capacity. The pseudo-second-order model successfully described the kinetic of Cu(II) adsorption by KAHHAC. The adsorbed Cu(II) onto KAHHAC was completely desorbed by 0.5?M nitric acid. In conclusion, HH activated carbon (AC) produced by the potassium acetate activation method is a very useful and efficient sorbent material for the removal of Cu(II) from aqueous solution.