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Previous RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.

The conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.

Numerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.

The strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.

This study examines the effects of CLS and DS on companies' WCME and analyses the differences in WCME at company and market levels.

This study adopts the DEA approach, regression, differences, and additional analyses to achieve its objectives. This study employs 235 non-financial companies and 1,175 company-year observations from eight active industries in the United States from 2016 to 2020.

The findings indicate that CLS and DS strategies positively influence companies' WCME. Additionally, WCME differed across size categories and industries, with large companies and those operating in the communication services industry showing better WCME. By contrast, WCME did not differ between the periods before and during the COVID-19 pandemic.

This study scrutinizes the impact of CLS and DS strategies on companies' WCME to bridge the gap in this field. It extends the investigation of competitive strategies as explanatory variables for a company's WCME and examines the differences in companies' WCME at the company and market levels, which may assist decision-makers in improving their strategies and efficiencies for continuous improvement.

This study enhances current knowledge by uncovering the influence of CLS and DS strategies on improving companies' WCME, an underexplored topic. It also explores companies' WCME trends and patterns regarding company size, industry type, and the pandemic period to draw interesting conclusions about the essence of WCME.