scholarly journals On the Construction of Converging Hierarchies for Polynomial Optimization Based on Certificates of Global Positivity

2019 ◽  
Vol 44 (4) ◽  
pp. 1192-1207 ◽  
Author(s):  
Amir Ali Ahmadi ◽  
Georgina Hall
Keyword(s):  
20Th Century ◽  
Lower Bounds ◽  
Polynomial Optimization ◽  
Sum Of Squares ◽  
Late 20Th Century ◽  
Minimization Problems ◽  
General Polynomial ◽  
Feasible Sets ◽  
Diagonally Dominant ◽  
Inner Approximation

In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity. At their heart, these hierarchies rely crucially on Positivstellensätze from the late 20th century (e.g., due to Stengle, Putinar, or Schmüdgen) that certify positivity of a polynomial on an arbitrary closed basic semialgebraic set. In this paper, we show that such hierarchies could in fact be designed from much more limited Positivstellensätze dating back to the early 20th century that only certify positivity of a polynomial globally. More precisely, we show that any inner approximation to the cone of positive homogeneous polynomials that is arbitrarily tight can be turned into a converging hierarchy of lower bounds for general polynomial minimization problems with compact feasible sets. This in particular leads to a semidefinite programming–based hierarchy that relies solely on Artin’s solution to Hilbert’s 17th problem. We also use a classical result from Pólya on global positivity of even forms to construct an “optimization-free” converging hierarchy for general polynomial minimization problems with compact feasible sets. This hierarchy requires only polynomial multiplication and checking nonnegativity of coefficients of certain fixed polynomials. As a corollary, we obtain new linear programming–based and second-order cone programming–based hierarchies for polynomial minimization problems that rely on the recently introduced concepts of diagonally dominant sum of squares and scaled diagonally dominant sum of squares polynomials. We remark that the scope of this paper is theoretical at this stage, as our hierarchies—though they involve at most two sum of squares constraints or only elementary arithmetic at each level—require the use of bisection and increase the number of variables (respectively, the degree) of the problem by the number of inequality constraints plus three (respectively, by a factor of two).

“Band Wagon and Gravy Train”: uses and abuses along the Silk Road

Afghanistan ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 171-194
Author(s):  
Warwick Ball
Keyword(s):  
20Th Century ◽  
21St Century ◽  
Silk Road ◽  
Late 20Th Century ◽  
Ancient Trade ◽  
International Image ◽  
Academic Discussion ◽  
The Silk Road

The Silk Road as an image is a relatively new one for Afghanistan. It appeals to both the pre-Islamic and the perceived Islamic past, thus offering an Islamic balance to previous identities linked to Bamiyan or to the Kushans. It also appeals to a broader and more international image, one that has been taken up by many other countries. This paper traces the rise of the image of the Silk Road and its use as a metaphor for ancient trade to encompass all contacts throughout Eurasia, prehistoric, ancient and modern, but also how the image has been adopted and expanded into many other areas: politics, tourism and academia. It is argued here that the origin and popularity of the term lies in late 20th century (and increasingly 21st century) politics rather than any reality of ancient trade. Its consequent validity as a metaphor in academic discussion is questioned

scholarly journals Run to the hills: Forest growth responsiveness to drought increased at higher elevation during the late 20th century

2021 ◽  
Vol 772 ◽  
pp. 145286
Author(s):  
Marín Pompa-García ◽  
Marcos González-Cásares ◽  
Antonio Gazol ◽  
J. Julio Camarero
Keyword(s):  
20Th Century ◽  
Forest Growth ◽  
Late 20Th Century

scholarly journals Urban Policies and Large Projects in Central City Areas: The Example of Madrid (Spain)

Urban Science ◽  
2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
Dolores Brandis García
Keyword(s):  
Urban Planning ◽  
20Th Century ◽  
Large Scale ◽  
Central City ◽  
Global Market ◽  
Late 20Th Century ◽  
Public And Private ◽  
Urban Policies ◽  
Starting Point ◽  
The City

Since the late 20th century major, European cities have exhibited large projects driven by neoliberal urban planning policies whose aim is to enhance their position on the global market. By locating these projects in central city areas, they also heighten and reinforce their privileged situation within the city as a whole, thus contributing to deepening the centre–periphery rift. The starting point for this study is the significance and scope of large projects in metropolitan cities’ urban planning agendas since the final decade of the 20th century. The aim of this article is to demonstrate the correlation between the various opposing conservative and progressive urban policies, and the projects put forward, for the city of Madrid. A study of documentary sources and the strategies deployed by public and private agents are interpreted in the light of a process during which the city has had a succession of alternating governments defending opposing urban development models. This analysis allows us to conclude that the predominant large-scale projects proposed under conservative policies have contributed to deepening the centre–periphery rift appreciated in the city.

scholarly journals Place matters: geographical context, place belonging and the production of locality in Mediterranean Noirs

GeoJournal ◽  
2021 ◽  
Author(s):  
Nicola Gabellieri
Keyword(s):  
20Th Century ◽  
Crime Fiction ◽  
The Novel ◽  
Late 20Th Century ◽  
Literary Works ◽  
Geographical Discourse ◽  
Detective Stories ◽  
Narrative Medium ◽  
Geographical Context

AbstractScholars have been investigating detective stories and crime fiction mostly as literary works reflecting the societies that produced them and the movement from modernism to postmodernism. However, these genres have generally been neglected by literary geographers. In the attempt to fill such an epistemological vacuum, this paper examines and compare the function and importance of geography in both classic and late 20th century detective stories. Arthur Conan Doyle’s and Agatha Christie’s detective stories are compared to Mediterranean noir books by Manuel Montalbán, Andrea Camilleri and Jean Claude Izzo. While space is shown to be at the center of the investigations in the former two authors, the latter rather focus on place, that is space invested by the authors with meaning and feelings of identity and belonging. From this perspective, the article argues that detective investigations have become a narrative medium allowing the readership to explore the writer’s representation/construction of his own territorial context, or place-setting, which functions as a co-protagonist of the novel. In conclusion, the paper suggests that the emerging role of place in some of the later popular crime fiction can be interpreted as the result of writer’s sentiment of belonging and, according to Appadurai’s theory, as a literary and geographical discourse aimed at the production of locality.

Focusing on India’s Look East Policy: India–China relationship from 1947 to 2020

2021 ◽  
pp. 223386592110183
Author(s):  
Kaushik Roy
Keyword(s):  
20Th Century ◽  
Industrial Revolution ◽  
International System ◽  
China Policy ◽  
Economic Competition ◽  
Intimate Contact ◽  
Late 20Th Century ◽  
Republic Of China ◽  
China And India ◽  
The World

Before the onset of the industrial revolution, China and India were the two biggest powers in Eurasia. Their total population comprised almost half of the world’s population. And the GNP of premodern China was half of the combined GNP of the world. Before circa 1600 CE, most of the textiles and iron in the world were manufactured in these two countries. China and India suffered a temporary eclipse during the age of colonialism. However, with the rise of the economic and military power of China and India from the late 20th century, it seems that these two countries are bound to reclaim their traditional positions as big powers in the international system. However, there is a caveat. In the premodern era, the Himalayas prevented any intimate contact between the ‘dragon’ and the ‘elephant’. But, from the mid-20th century, advances in technology, economic competition and the annexation of Tibet by the People’s Republic of China (PRC) among other factors resulted in China and India coming into direct contact with each other. The result has been cooperation–competition–conflict. And this has had consequences not only for these two countries but for the whole world. The present article attempts to trace the troubled trajectory of India’s China policy from the late 1940s (when these two countries became independent) up to the present day.

Did We Finally Slay the Evil Dragon of Cigarette Smoking in the Late 20th Century?

CHEST Journal ◽  
2014 ◽  
Vol 146 (6) ◽  
pp. 1438-1443 ◽  
Author(s):  
Richard D. Hurt ◽  
Joseph G. Murphy ◽  
William F. Dunn
Keyword(s):  
Cigarette Smoking ◽  
20Th Century ◽  
Late 20Th Century

scholarly journals Micro: An International Open Access Journal for All of Microscale and Nanoscale Science

Micro ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 1-2
Author(s):  
Eiichi Tamiya
Keyword(s):  
Open Access ◽  
20Th Century ◽  
Special Interest ◽  
Biological Properties ◽  
Open Access Journal ◽  
Length Scale ◽  
Late 20Th Century ◽  
Physical Chemical ◽  
Nanoscale Science

Since the late 20th century, there has been a special interest in the microscale and nanoscale research investigating and exploiting the physical, chemical, and biological properties of these length-scale systems [...]

Sign in / Sign up

Export Citation Format

Share Document