In this paper, we present a semi-proximal alternating direction method of multipliers (ADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed semiproximal ADMM for the step-length τ ∈ (0, (1+ √ 5)/2) and the penalty parameter σ ∈ (0, +∞). In particular, if σ > 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block semi-proximal ADMM reduces to the directly extended 3-block ADMM with τ ∈ (0, (1 + √ 5)/2).

HighlightsOMMT/paraffin composite PCM were prepared.OMMT/paraffin/grafted MWNT composite phase change material.Paraffin is intercalated into the interlayer of OMMT.OMMT/paraffin/grafted MWNT has stable thermal properties.OMMT/paraffin/grafted MWNT has a better heat storage prosperity.

We contend that generalizability (G) theory allows the design of psychometric approaches to testing English‐language learners (ELLs) that are consistent with current thinking in linguistics. We used G theory to estimate the amount of measurement error due to code (language or dialect). Fourth‐ and fifth‐grade ELLs, native speakers of Haitian‐Creole from two speech communities, were given the same set of mathematics items in the standard English and standard Haitian‐Creole dialects (Sample 1) or in the standard and local dialects of Haitian‐Creole (Samples 2 and 3). The largest measurement error observed was produced by the interaction of student, item, and code. Our results indicate that the reliability and dependability of ELL achievement measures is affected by two facts that operate in combination: Each test item poses a unique set of linguistic challenges and each student has a unique set of linguistic strengths and weaknesses. This sensitivity to language appears to take place at the level of dialect. Also, students from different speech communities within the same broad linguistic group may differ considerably in the number of items needed to obtain dependable measures of their academic achievement. Whether students are tested in English or in their first language, dialect variation needs to be considered if language as a source of measurement error is to be effectively addressed.