Monotonicity for Multiobjective Accelerated Proximal Gradient Methods

Accelerated proximal gradient methods, which are also called fast iterative shrinkage-thresholding algorithms (FISTA) are known to be efficient for many applications. Recently, Tanabe et al. proposed an extension of FISTA for multiobjective optimization problems. However, similarly to the single-objective minimization case, the objective functions values may increase in some iterations, and inexact computations of subproblems can also lead to divergence. Motivated by this, here we propose a variant of the FISTA for multiobjective optimization, that imposes some monotonicity of the objective functions values. In the single-objective case, we retrieve the so-called MFISTA, proposed by Beck and Teboulle. We also prove that our method has global convergence with rate $O(1/k^2)$, where $k$ is the number of iterations, and show some numerical advantages in requiring monotonicity.Comment: - Added new numerical experiment

An accelerated proximal gradient method for multiobjective optimization

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalarization has been widely studied, but providing accelerated methods with accurate proofs of convergence rates remains an open problem. Our proposed method is a multiobjective generalization of the accelerated proximal gradient method, also known as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), for scalar optimization. The key to this successful extension is solving a subproblem with terms exclusive to the multiobjective case. This approach allows us to demonstrate the global convergence rate of the proposed method ($O(1 / k^2)$), using a merit function to measure the complexity. Furthermore, we present an efficient way to solve the subproblem via its dual representation, and we confirm the validity of the proposed method through some numerical experiments

Experimental Assessment on Performance of a Heat Pump Cycle Using R32/R1234yf and R744/R32/R1234yf

     Hydro-fluorocarbons (HFCs) are widely used as working fluids (refrigerants) in air-conditioning and refrigeration systems. However, at the 1997 Kyoto Conference (COP3), it was determined that the product and use of HFCs should be regulated due to their high global warming potential (GWP). In the above mentioned situation for the air-conditioning and refrigeration systems, recently, R1234yf having extremely low-GWP was nominated as one of the alternates of HFCs. Some literatures reported that the heating capacity of heat pump cycles using R1234yf is less than R410A because of its smaller vapor density and latent heat. To achieve the performance comparable to R410A, much larger unit is required. Therefore, in this present study, mixing with R32 of larger latent heat and relatively low-GWP into R1234yf was attempted. Additionally, R744 having higher vapor density and extremely low-GWP was added into R32/R1234yf.  The R32/R1234yf and R744/R32/R1234yf are zeotropic mixtures that cause temperature change during the phase-change, typically called temperature glide. When this temperature glide is utilized effectively to decrease the irreversible loss in heat exchanger, the cycle performance can be improved. The degree of temperature glide is determined by the composition of refrigerant mixtures. The composition of the test refrigerants are selected from the criterions of GWPs just below 300 and 200.Experiment was conducted with a vapor compression heat pump cycle using a compressor developed for R410A. The condenser and the evaporator are tube-in tube heat exchangers of counter-flow configuration.  At compositions with GWP200 and a given heating capacity, the COP of R32/R1234yf and R744/R32/R1234yf are lower than that of R410A. The main causes were that R32/R1234yf of GWP200 has lower vapor density and R744/R32/R1234yf of GWP200 has lager temperature glide. At compositions with GWP300, R32/R1234yf and R744/R32/R1234yf exhibit comparable COP and heating capacity to R410A. Using R32/R1234yf and R744/R32/R1234yf of compositions with GWP300, as the alternatives of R410A, is feasible idea

ラット大脳皮質における電位オシレーターを駆動するための状況に応じた戦略

Information integration in the brain requires functional connectivity between local neural networks. Here, we investigated the interregional coupling mechanism from the viewpoint of oscillations using optical recording methods. Low-frequency electrical stimulation of rat neocortical slices in a caffeine-containing medium induced oscillatory activity between the primary visual cortex (Oc1) and medial secondary visual cortex (Oc2M), in which the oscillation generator was located in the Oc2M and was triggered by a feedforward signal. During to-and-fro oscillatory activity, neural excitation was marked in layer II/III. When the upper layer was disrupted between Oc1 and Oc2M, feedforward signals could propagate through the deep layer and switch on the oscillator in the Oc2M. When the lower layer was disrupted between Oc1 and Oc2M, feedforward signals could propagate through the upper layer and switch on the oscillator in the Oc2M. In the backward direction, neither the upper layer cut nor the lower layer cut disrupted the propagation of the oscillations. In all cases, the horizontal and vertical pathways were used as needed. Fluctuations in the oscillatory waveforms of the local field potential at the upper and lower layers in the Oc2M were reversed, suggesting that the oscillation originated between the two layers. Thus, the neocortex may work as a safety device for interregional communications in an alternative way to drive voltage oscillators in the neocortex

Sr3(Al3+xSi13−x)(N21−xO2+x):Eu2+ (x ∼ 0): a monoclinic modification of Sr-sialon

The structure of the title compound, Sr-bearing oxonitrido­aluminosilicate (Sr-sialon), contains two types of channels running along the a axis, with the three unique Sr atoms (coordinatioon number seven) residing in the larger one. The channels cross a three-dimensional Si–Al–O–N network, in which the Si and Al atoms are in a tetra­hedral coordination with N and O atoms. The chemical composition of the crystal is close to Sr3Al3Si13N21O2 (tris­trontium trialuminium trideca­silicon henicosa­nitride dioxide), which can be expressed as a mixture of SrSiN2, Si3N4, AlN, and SiO2 components in the molar ratio 3:3:3:1. The crystal studied was metrically orthorhombic, consisting of four twin components related by metric merohedry