Considered here are extremal convolutions concerned with allocative efficiency, risk sharing, or market equilibrium. Each additive term is upper semicontinuous, proper concave, maybe non-smooth, and possibly extended-valued. In a leading interpretation, each term, alongside its block of coordinates, is controlled by an independent economic agent. Vectors are construed as contingent claims or as bundles of commodities. These are diverse, divisible, and perfectly transferable. At every stage two randomly selected agents make bilateral direct exchanges. The amounts transferred between the two parties depend on the difference between their generalized gradients. The resulting process—and the associated convergence analysis—fits the frames of stochastic programming. Motivation stems from exchange markets.
This is a preview of subscription content, log in to check access.
Thanks for support are due the department and Røwdes Fond.
Benveniste A, Métivier M, Priouret P (1990) Adaptive algorithms and stochastic approximations. Springer, BerlinCrossRefGoogle Scholar
Cockerell HAL, Green E (1976) The British Insurance Business. Sheffield Academic Press, SheffieldGoogle Scholar
Eeckhoudt L, Gollier C, Schlesinger H (2005) Economic and financial decisions under risk. Princeton University Press, PrincetonGoogle Scholar
Feldman AM (1973) Bilateral trading processes, pair-wise optimality, and Pareto optimality. Rev Econ Stud 4:463–473CrossRefGoogle Scholar
Flåm SD (2016a) Bilateral exchange and competitive equilibrium. Set-Valued Var Anal 24:1–11CrossRefGoogle Scholar
Flåm SD (2016b) Borch’s theorem, equal margins, and efficient allocations. Insur Math Econ 70:162–168CrossRefGoogle Scholar
Flåm SD, Gramstad K (2012) Direct exchange in linear economies. Int Game Theory Rev 14:4CrossRefGoogle Scholar
Gaivoronski AA (1994) Convergence properties of backpropagation for neural nets via theory of stochastic gradient methods. Optim Methods Softw 4(2):117–134CrossRefGoogle Scholar
Hiriart-Urruty J-B (2012) Bases, outils et principes pour l’analyse variationelle. Springer, BerlinGoogle Scholar
Hiriart-Urruty J-B, Marechal C (1993) Convex analysis and minimization algorithms I. Springer, BerlinCrossRefGoogle Scholar
Hua X, Yamashita N (2016) Block coordinate proximal gradient methods for nonsmooth separable optimization. Math Program Ser A 160:1–32CrossRefGoogle Scholar
Lengwiler Y (2004) Microfoundations of financial economics. Princeton University Press, PrincetonGoogle Scholar
Necoara I (2013) Random coordinate descent algorithms for multi-agent convex optimization over networks. IEEE Trans Autom Control 58(8):2001–2013CrossRefGoogle Scholar
Necoara I, Patrascu A (2014) A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints. Comput Optim Appl 57(2):307–337CrossRefGoogle Scholar
Necoara I, Nesterov Yu, Glineur F (2017) Random block coordinate descent methods for linearly constrained optimization over networks. J Optim Theory Appl 173:227–2354CrossRefGoogle Scholar
Nesterov Yu (2012) Efficiency of coordinate descent methods on huge-scale optimization problems. SIAM J Optim 22(2):341–362CrossRefGoogle Scholar
Nesterov Yu, Shikhman V (2017) Distributed price adjustment based on convex analysis. J Optim Theory Appl 172:594–622CrossRefGoogle Scholar