In this paper, we study distributionally robust optimization approaches for a one-stage stochastic minimization problem, where the true distribution of the underlying random variables is unknown but ...it is possible to construct a set of probability distributions, which contains the true distribution and optimal decision is taken on the basis of the worst-possible distribution from that set. We consider the case when the distributional set (which is also known as the ambiguity set) varies and its impact on the optimal value and the optimal solutions. A typical example is when the ambiguity set is constructed through samples and we need to look into the impact of increasing the sample size. The analysis provides a unified framework for convergence of some problems where the ambiguity set is approximated in a process with increasing information on uncertainty and extends the classical convergence analysis in stochastic programming. The discussion is extended briefly to a stochastic Nash equilibrium problem where each player takes a robust action on the basis of the worst subjective expected objective values.
In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate ...conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We explain how the discretized two-stage SLCP may be solved by the well-known progressive hedging method (PHM). Moreover, we extend the discussion by considering a two-stage distributionally robust LCP (DRLCP) with moment constraints and proposing a discretization scheme for the DRLCP. As an application, we show how the SLCP and DRLCP models can be used to study equilibrium arising from two-stage duopoly game where each player plans to set up its optimal capacity at present with anticipated competition for production in future.
We propose a formulation of the distributionally robust variational inequality (DRVI) to deal with uncertainties of distributions of the involved random variables in variational inequalities. ...Examples of the DRVI are provided, including the optimality conditions for distributionally robust optimization and distributionally robust games (DRG). The existence of solutions and monotonicity of the DRVI are discussed. Moreover, we propose a sample average approximation (SAA) approach to the DRVI and study its convergence properties. Numerical examples of DRG are presented to illustrate solutions of the DRVI and convergence properties of the SAA approach.
In this paper, we consider the sample average approximation (SAA) approach for a class of stochastic nonlinear complementarity problems (SNCPs) and study the corresponding convergence properties. We ...first investigate the convergence of the SAA counterparts of two-stage SNCPs when the first-stage problem is continuously differentiable and the second-stage problem is locally Lipschitz continuous. After that, we extend the convergence results to a class of multistage SNCPs whose decision variable of each stage is influenced only by the decision variables of adjacent stages. Finally, some preliminary numerical tests are presented to illustrate the convergence results.
Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see Rockafellar and Wets (Math. Oper. Res. 16:119–147, 1991), Ruszczyński and ...Shapiro (Stochastic Programming, Handbook in OR & MS, North-Holland Publishing Company, Amsterdam, 2003) and Ruszczyński (Math. Program. 79:333–353, 1997). In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. This is achieved by introducing nonanticipativity constraints for the first stage decision variables, rearranging the minimax problem through Lagrange decomposition and applying the well-known primal-dual hybrid gradient (PDHG) method to the new minimax problem. The algorithmic framework does not depend on specific structure of the ambiguity set. To extend the algorithm to the case that the underlying random variables are continuously distributed, we propose a discretization scheme and quantify the error arising from the discretization in terms of the optimal value and the optimal solutions when the ambiguity set is constructed through generalized prior moment conditions, the Kantorovich ball and
ϕ
-divergence centred at an empirical probability distribution. Some preliminary numerical tests show the proposed decomposition algorithm featured with parallel computing performs well.
Many research works have demonstrated that the combination of atomically precise cluster deposition and theoretical calculations is able to address fundamental aspects of size-effects, ...cluster-support interactions, and reaction mechanisms of cluster materials. Although the wet chemistry method has been widely used to synthesize nanoparticles, the gas-phase synthesis and size-selected strategy was the only method to prepare supported metal clusters with precise numbers of atoms for a long time. However, the low throughput of the physical synthesis method has severely constrained its wider adoption for catalysis applications. In this review, we introduce the latest progress on three types of cluster source which have the most promising potential for scale-up, including sputtering gas aggregation source, pulsed microplasma cluster source, and matrix assembly cluster source. While the sputtering gas aggregation source is leading ahead with a production rate of ∼20 mg·h
−1
, the pulsed microplasma source has the smallest physical dimensions which makes it possible to compact multiple such devices into a small volume for multiplied production rate. The matrix assembly source has the shortest development history, but already show an impressive deposition rate of ~10 mg·h
−1
. At the end of the review, the possible routes for further throughput scale-up are envisaged.
Piezoelectric actuator has the advantages of high rigidity, wide bandwidth, fast response and high resolution. Therefore, they are widely used in many micro and nano positioning applications. ...However, the hysteresis characteristic in the piezoelectric actuator (PEA) seriously affects its positioning accuracy and even causes instability. In this paper, a modified Prandtl-Ishlinskii (MPI) model, which can describe the rate asymmetric hysteresis of piezoelectric actuator, is studied. The hysteresis compensation is realized by using the rate dependent Prandtl-Iishlinskii model based on the improved Prandtl-Iishlinskii hysteresis model and the hysteresis characteristics of the driver measured in the laboratory under the frequency input of up to 100 Hz. In order to further reduce the error of feedforward compensation, a sliding mode controller is designed. The stability of the control system is proved by Lyapunov theory. The experimental results show that the linear error of the system is reduced from 10% to less than 1%, and the tracking error can also be reduced by 90%.
Electrical engineering; Physics; Piezoelectric actuator, Precision positioning, Hysteresis, Prandtl-Ishlinskii.
Steel Circular Hollow Section (CHS) joints have been extensively utilized in construction. Current research mainly focuses on joints reinforced in unloaded states, reinforcement under load less ...commonly addressed. This study examines the mechanical behavior of CHS T-joints through an experimental analysis of six specimens, each featuring varying brace-to-chord diameter ratios (β), welded under different load factors. Identified primary failure modes of the joints are local buckling and out-of-plane inclination. Furthermore, a thermo-mechanical coupling finite element model, considering the material addition during the welding process, was developed to investigate the influence of the welding under load. The results indicate that welding under axial load has little effect on the ultimate loading capacity of the CHS T-joints. Notably, welding-induced residual deformation on the chord surpasses that on the brace, particularly when welding passes are proximal to the brace-chord intersection. Residual stress in welds is not significantly affected by the stress in the tubular; only the stiffeners near the welds are affected. Despite some joints exhibiting out-of-plane inclination, the enhancement in ultimate bearing capacity exceeds 24%.
The two most important issues that plague wider use of stainless steel bipolar plates in polymer electrolyte membrane fuel cells (PEMFCs) are insufficient corrosion resistance and surface ...conductivity. In this study, C/CrN multilayer coatings are deposited on 316L stainless steel samples by close-field unbalanced magnetron sputtering ion plating. SEM shows that the C/CrN coatings are dense, continuous, and composing of carbon granules on the surface. Raman spectroscopy reveals an amorphous structure with a large sp2 constituent. The corrosion resistance and interfacial contact resistance (ICR) are investigated systematically. A superior ICR in the range of 2.6–2.9mΩ-cm2 at a compaction force of 150N/cm2 is achieved and it is even better than that of graphite. The deposited film possesses high chemical inertness thereby significantly enhancing the corrosion resistance of the coated SS316L. A thickness of 800nm is sufficient to protect against corrosion. C/CrN multilayer coatings are beneficial in that it can lead to a faster PVD deposition process and lower material cost, while permitting a superior performance in terms of surface conductivity and corrosion resistance.
► C/CrN multilayer coatings with dense structure and high percentage of sp2 bond are deposited on SS316L. ► C/CrN multilayer coatings exhibit superior surface conductivity that is even better than that of graphite. ► Electrochemical results disclose that the C/CrN multilayer coatings have excellent corrosion resistance.
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