Peaceman-Rachford splitting for a class of nonconvex optimization problems

We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is computable, then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem. We also give sufficient conditions guaranteeing boundedness of the sequence generated. We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems with a coercive objective that is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function; this setting covers a large class of nonconvex feasibility problems and constrained least squares problems. Finally, we illustrate the proposed algorithm numerically

TESTING FOR COMPLETE PASS-THROUGH OF EX ASS-THROUGH OF EXCHANGE RA ANGE RATE WITHOUT TRADE BARRIERS

The objective of this paper is to test whether the complete pass-through of exchange rate exists when there are almost no transaction costs and in the environment of competitive market. In general, the literature claims that the pass-through of exchange rate is incomplete due to imperfect market, i.e. the presence of transaction costs and imperfect competition. The quasi-experimental case of the food import to Hong Kong from Mainland China is considered in the analysis. The results show that the pass-through of the exchange rate of Chinese RMB against to US dollar to Hong Kong\u27s food import price is complete in long-run equilibrium. Besides, the short-run adjustment significantly contributes to correcting the deviation from the long-run pass-through effect. Moreover, the complete pass-through still exists after accounting for the effects of asymmetry and volatility. Therefore, this paper contributes to the literature by providing empirical evidence that the complete pass-through of exchange rate can exist in the real world

A Forest from the Trees: Generation through Neighborhoods

In this work, we propose to learn a generative model using both learned features (through a latent space) and memories (through neighbors). Although human learning makes seamless use of both learned perceptual features and instance recall, current generative learning paradigms only make use of one of these two components. Take, for instance, flow models, which learn a latent space of invertible features that follow a simple distribution. Conversely, kernel density techniques use instances to shift a simple distribution into an aggregate mixture model. Here we propose multiple methods to enhance the latent space of a flow model with neighborhood information. Not only does our proposed framework represent a more human-like approach by leveraging both learned features and memories, but it may also be viewed as a step forward in non-parametric methods. The efficacy of our model is shown empirically with standard image datasets. We observe compelling results and a significant improvement over baselines

A CFD-based scaling analysis on liquid and paint droplets moving through a weak concurrent airflow stream

We conducted volume of fluids (VOF) multiphase model numerical simulations to obtain the interaction among all the major governing forces identified in our previous paper. Our numerical experiments are intended to assess the droplet generation process and the jetting behavior by providing specific input conditions, offering CFD as a tool to study scaling correlations instead of physical experiments. Water droplets that can represent waterborne paints were generated by piezo-generated sinusoidal waveforms at the inlet of the nozzle. The governing forces included the external piezo-based wave-generation force, the inertial force of droplets, the inertial force of air, the viscose force of air acting on droplet surface, the viscous force of liquid, and surface tension force of droplets. The law approach-based scaling theory was applied to explain the significance of traditional pi-numbers, such as the Reynolds number, Strouhal number, Weber number, Capillary number, and Ω, in predicting the performance of the inkjet nozzle before introducing the operating conditions