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INTEGRAL PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter deals with integral problems. Using examples, it illustrates the need to use weak topologies to obtain compactness and coerciveness conditions. The sufficiency and necessity of the ... More


Differentials and Convex Analysis

Robert G. Chambers

in Competitive Agents in Certain and Uncertain Markets

Published in print:
2021
Published Online:
December 2020
ISBN:
9780190063016
eISBN:
9780190063047
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190063016.003.0002
Subject:
Economics and Finance, Econometrics, Microeconomics

Mathematical tools necessary to the argument are presented and discussed. The focus is on concepts borrowed from the convex analysis and variational analysis literatures. The chapter starts by ... More


Quadratic Surplus

Alfred Galichon

in Optimal Transport Methods in Economics

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691172767
eISBN:
9781400883592
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691172767.003.0006
Subject:
Economics and Finance, Microeconomics

This chapter considers the case when the attributes are d-dimensional vectors and the surplus is the scalar product; it assumes that the distribution of the workers' attributes is continuous, but it ... More


Minimax Theorem

João P. Hespanha

in Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175218
eISBN:
9781400885442
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175218.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter deals with the Minimax Theorem and its proof, which is based on elementary results from convex analysis. The theorem states that for every matrix A, the average security levels of both ... More


More General Surplus

Alfred Galichon

in Optimal Transport Methods in Economics

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691172767
eISBN:
9781400883592
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691172767.003.0007
Subject:
Economics and Finance, Microeconomics

This chapter considers a case with a more general surplus function. It shows that when the scalar-product surplus is replaced by a more general function, much of the machinery put in place in Chapter ... More


Optimal Transport Methods in Economics

Alfred Galichon

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691172767
eISBN:
9781400883592
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691172767.001.0001
Subject:
Economics and Finance, Microeconomics

Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the ... More


Competitive Agents in Certain and Uncertain Markets

Robert G. Chambers

Published in print:
2021
Published Online:
December 2020
ISBN:
9780190063016
eISBN:
9780190063047
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190063016.001.0001
Subject:
Economics and Finance, Econometrics, Microeconomics

This book uses concepts from optimization theory to develop an integrated analytic framework for treating consumer, producer, and market equilibrium analyses as special cases of a generic ... More


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