The conjugate gradient method is one of the most important ideas in sci-entific computing. It is applied to solving linear systems of equations and nonlinear optimization problems. In this paper, based on a variant of the Hestenes–Stiefel (HS) method and Polak–Ribière–Polyak (PRP) method, two modified conjugate gradient methods (named MHS∗ and MPRP∗) are presented and analyzed. The search direction of the presented methods fulfills the sufficient descent condition at each iteration. We establish the Global convergence of the proposed algorithms under normal assumptions and strong Wolfe line search. Preliminary elementary numerical experi-ment results are presented, demonstrating the promise and the effective-ness of the proposed methods. Finally, the proposed methods are further extended to solve the problem of conditional model regression function.

Background: Vaccine hesitancy is a Global problem with diverse local policy responses, from voluntaristic to coercive. Between 2015 and 2017, California, Australia, France, and Italy increased the coerciveness of their childhood vaccine regimes. Despite this apparent convergence, there is little evidence of imposition, policy learning, or diffusion –,the drivers that are usually discussed in scholarly literature on policy convergence. The fact that the four governments were oriented across the political spectrum, with quite different political and institutional systems, further indicates an empirical puzzle. Methods: To better understand the drivers of enhanced vaccine mandates, a crucial issue during the coronavirus disease 2019 (COVID-19) Global rollout, this article engages with four case studies assembled from qualitative analysis of semistructured in-country interviews and document analysis between November 2018 and November 2020. Key informants had specific expert knowledge or played a role in the introduction or implementation of the new policies. Interview transcripts were coded inductively and deductively, augmented with extensive analysis of legal, policy, academic and media documents. Results: The case analysis identifies two key and interacting elements in government decisions to tighten vaccine mandates: functional and political pressures. Policy-makers in Italy and France were primarily driven by functional challenges, with their vaccination governance systems under threat from reduced population compliance. California and Australia did not face systemic threats to the functioning of their systems, but activists utilised local opportunities to heighten political pressure on decision makers. Conclusion: In four recent cases of high-income jurisdictions making childhood vaccination policies more coercive, vaccine hesitancy alone could not explain why the policies arose in these jurisdictions and not others, while path dependency alone could not explain why some jurisdictions with mandates made them more coercive. Explanation lies in restrictive mandates being attractive for governments, whether they face systemic functional problems in vaccine governance, or political pressures generated by media and activists. Mandates can be framed as targeting whole populations or localised groups of refusers, and implemented without onerous costs or policy complexity.

Global Health 2035, the report of The Lancet Commission on Investing in Health, laid out a bold, highly ambitious framework for making rapid progress in improving Global public health outcomes. It showed that with the right health investments, the international community could achieve a “grand convergence” in Global health-a reductionin avertable infectious, maternal, and child deaths down to universally low levels-within a generation. Rwanda’s success in rapidly reducing such deaths over the last 20 years shows that convergence is feasible. Binagwaho and Scott have argued that 5 lessons from this success are the importance of equity, quality health services, evidence-informed policy, intersectoral collaboration, and effective collaboration between countries and multilateral agencies. This article re-examines these lessons through the lens of the Global Health 2035 report to analyze how the experience in Rwanda might be generalized for other countries to making progress towards achieving a grand convergence.