Implementing a smooth exact penalty function for equality-constrained nonlinear optimization

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate that the computational kernels required are no more expensive than other widely accepted methods for nonlinear optimization. The main kernel required to evaluate the penalty function and its derivatives is solving a structured linear system. We show how to solve this system efficiently by storing a single factorization each iteration when the matrices are available explicitly. We further show how to adapt the penalty function to the class of factorization-free algorithms by solving the linear system iteratively. The penalty function therefore has promise when the linear system can be solved efficiently, e.g., for PDE-constrained optimization problems where efficient preconditioners exist. We discuss extensions including handling simple constraints explicitly, regularizing the penalty function, and inexact evaluation of the penalty function and its gradients. We demonstrate the merits of the approach and its various features on some nonlinear programs from a standard test set, and some PDE-constrained optimization problems

Do emerging market business groups outperform at exporting?

Business groups (BGs) are collections of legally independent multi-business entities coordinated through a central entity. They primarily operate in emerging markets, prominent examples being Samsung, Hyundai, and Tata Group. BG are widely viewed as an efficiency-enhancing organizational form that internalizes transactions across affiliates: this can increase the efficiency of resource allocation, especially in contexts where high transaction costs limit arms-length transactions through markets. Hence, with their superior access to resources, notably capital, knowledge and labour, BGs can support their affiliated firms to improve their performance. But, do their advantages extend to international markets: are they better exporters than non-affiliated firms

Why business groups (think Samsung or Tata Group) have an export advantage in emerging markets

With their superior access to capital, knowledge and labour, business groups offer many advantages to their affiliated firms. Daniel Shapiro, Saul Estrin, Michael Carney and Zhixiang (Steven) Liang write that these advantages extend to international markets, as group members are better exporters than non-affiliated firms. They also show that business group advantages are greater as market institutions strengthen and reduced when political institutions are more democratic

Are Latin American business groups different? An exploratory international political economy perspective

Purpose: This study aims to advance an international political economy (IPE) perspective that geo-political events can have long-lasting imprint effects on countries and their firms. The study also aims to explore the idea that shared political history and geography combine to create specific structural conditions that shape the international competitiveness of all firms in a region. In particular, the authors consider whether the Monroe Doctrine of 1823, which asserted American influence in the Western Hemisphere, contributed to the creation of institutional structures across Latin America (LA) affecting the strategies of all firms to this day. The authors also illustrate the IPE perspective using the example of the contemporary international competitiveness of LA business groups. Design/methodology/approach: The authors illustrate the IPE perspective using the example of the contemporary international competitiveness of LA business groups. The exploratory framework of this study leads to a proposition about the export performance of Latin American business group affiliates. The authors use firm-level performance data for 32,000 firms across emerging economies to explore the proposition empirically while controlling for alternative explanations. To do this, the authors draw on the World Bank Economic Surveys. Findings: The authors derive a proposition that argues the Monroe Doctrine has had a long-run imprint effect on economic policymaking in LA, resulting in a common, persistent and negative impact on the international competitiveness of firms. The authors find strong and consistent evidence that in terms of export performance, all Latin American firms export less and group affiliates do not outperform independent firms, This finding contrasts with the results for all the other emerging market regions around the world. Research limitations/implications: The main contribution of this study has been to suggest the potential importance of shared regional geopolitical history and geography in explaining firm-level outcomes. However, this study is preliminary and introductory, although the authors seek to control for alternative country-specific explanations of the results. The analysis considers the effects of one particular IPE phenomenon, the Monroe Doctrine, in one particular location: LA. Future work should seek to contrast LA with other geopolitical security and alternative IPE structures. They might also address the time dimension from a historical perspective: is imprinting in LA driven by the length of the Monroe Doctrine arrangements? Practical implications: The most important managerial learning point concerns the relevance of geography and political economy factors for multinational enterprises strategy formation. There is widespread understanding that context is an important determinant of subsidiaries’ performance, and that strategies need to be constructed to take account of country-specific characteristics, most importantly, in emerging economies and institutional arrangements. This paper proposes that managers also need to take account of IPE structures, including security arrangements, and to consider the resulting regional as well as national context. Social implications: The analysis suggests that not only the performance of firms, including emblematic firms, but also the socially beneficial spillovers that might be generated from them, are contingent on the regional as well as national characteristics. Thus, business groups in most emerging economies are found to yield better performance and to provide higher levels of social impact, including concerning ESG goals. However, the findings of this study suggest that the former is not true for LA, which, the authors argue, is a consequence of imprinting as a result of the Monroe Doctrine. Further work is needed to establish whether the latter effect is also not true, but if that is the case, then regionally specific policies may be required to address the resulting corporate social shortfalls. Originality/value: The core idea is that geo-political events can have long-lasting imprint effects on countries and their firms: that shared political history and geography create specific structural conditions that shape the international competitiveness of all firms in a region. The authors explore this concept with reference to the Monroe Doctrine, asking whether its assertion of US influence across the Americas contributed to the creation of institutional structures across LA affecting the strategies of all firms to this day

The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that Computed Ground States of Two-Electron Atoms (and its 2010 Redux)

In order to appreciate how well off we mathematicians and scientists are today, with extremely fast hardware and lots and lots of memory, as well as with powerful software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and compare how things went then. We have chosen, as a case study, a problem that was considered a huge challenge at the time. Namely, we looked at C.L. Pekeris's seminal 1958 work on the ground state energies of two-electron atoms. We went through all the computations ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.Comment: 8 pages, 2 photos, final version as it appeared in the journa