Search results for "Subdifferentials"

showing 2 items of 2 documents

Prices and Pareto optima

2006

We provide necessary conditions for Pareto optimum in economies where tastes or technologies may be nonconvex, nonsmooth, and affected by externalities. Firms can pursue own objectives, much like the consumers. Infinite-dimensional commodity spaces are accommodated. Public goods and material balances are accounted for as special instances of linear restrictions.

Microeconomicsjel:C60first and second welfare theorem; weak and strong Pareto optimum; nonconvex tastes or technologies; public goods; externalities; local separation; subdifferentials; normal conesControl and OptimizationApplied Mathematicsjel:D60jel:D50EconomicsPareto principleManagement Science and Operations ResearchPublic goodCommodity (Marxism)ExternalityOptimization
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Subdifferential and conjugate calculus of integral functions with and without qualification conditions

2023

We characterize the subdifferential and the Fenchel conjugate of convex integral functions by means of respectively the approximate subdifferential and the conjugate of the associated convex normal integrands. The results are stated in Suslin locally convex spaces, and do not require continuity-type qualification conditions on the functions, nor special topological or algebraic structures on the index set. Consequently, when confined to separable Banach spaces, the characterizations of such a subdifferential are obtained using only the exact subdifferential of the given integrand but at nearby points. We also provide some simplifications of our formulas when additional continuity conditions…

Subdifferentialsconvex normal integrandsConvex normal integrandsSuslin spacessub-differentialsSuslin spaces. Mathematics Subject Classi…cation (2010): 26B0526J25[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]49H05Integral functions and functionals
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