05590nam 2200529 450 99646641470331620231110233030.03-030-72162-0(CKB)4100000011984432(MiAaPQ)EBC6682762(Au-PeEL)EBL6682762(OCoLC)1261380181(PPN)269149260(EXLCZ)99410000001198443220220411d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLectures on optimal transport /Luigi Ambrosio, Elia Brué, and Daniele SemolaCham, Switzerland :Springer,[2021]©20211 online resource (250 pages)Unitext ;v.1303-030-72161-2 Includes bibliographical references.Intro -- Preface -- Contents -- Lecture 1: Preliminary Notions and the Monge Problem -- 1 Notation and Preliminary Results -- 2 Monge's Formulation of the Optimal Transport Problem -- Lecture 2: The Kantorovich Problem -- 1 Kantorovich's Formulation of the Optimal Transport Problem -- 2 Transport Plans Versus Transport Maps -- 3 Advantages of Kantorovich's Formulation -- 4 Existence of Optimal Plans -- Lecture 3: The Kantorovich-Rubinstein Duality -- 1 Convex Analysis Tools -- 2 Proof of Duality via Fenchel-Rockafellar -- 3 The Theory of c-Duality -- 4 Proof of Duality and Dual Attainment for Bounded and Continuous Cost Functions -- Lecture 4: Necessary and Sufficient Optimality Conditions -- 1 Duality and Necessary/Sufficient Optimality Conditions for Lower Semicontinuous Costs -- 2 Remarks About Necessary and Sufficient Optimality Conditions -- 3 Remarks About c-Cyclical Monotonicity, c-Concavity and c-Transforms for Special Costs -- 4 Cost=distance2 -- 5 Cost=Distance -- 6 Convex Costs on the Real Line -- Lecture 5: Existence of Optimal Maps and Applications -- 1 Existence of Optimal Transport Maps -- 2 A Digression About Monge's Problem -- 3 Applications -- 4 Iterated Monotone Rearrangement -- Lecture 6: A Proof of the Isoperimetric Inequality and Stability in Optimal Transport -- 1 Isoperimetric Inequality -- 2 Stability of Optimal Plans and Maps -- Lecture 7: The Monge-Ampére Equation and Optimal Transport on Riemannian Manifolds -- 1 A General Change of Variables Formula -- 2 The Monge-Ampère Equation -- 3 Optimal Transport on Riemannian Manifolds -- Lecture 8: The Metric Side of Optimal Transport -- 1 The Distance W2 in P2(X) -- 2 Completeness of Square Integrable Probabilities -- 3 Characterization of Convergence in the Space of Square Integrable Probabilities.Lecture 9: Analysis on Metric Spaces and the Dynamic Formulation of Optimal Transport -- 1 Absolutely Continuous Curves and Their Metric Derivative -- 2 Geodesics and Action -- 3 Dynamic Reformulation of the Optimal Transport Problem -- Lecture 10: Wasserstein Geodesics, Nonbranching and Curvature -- 1 Lower Semicontinuity of the Action A2 -- 2 Compactness Criterion for Curves and Random Curves -- 3 Lifting of Geodesics from X to P2(X) -- Lecture 11: Gradient Flows: An Introduction -- 1 lambda-Convex Functions -- 2 Differentiability of Absolutely Continuous Curves -- 3 Gradient Flows -- Lecture 12: Gradient Flows: The Brézis-Komura Theorem -- 1 Maximal Monotone Operators -- 2 The Implicit Euler Scheme -- 3 Reduction to Initial Conditions with Finite Energy -- 4 Discrete EVI -- Lecture 13: Examples of Gradient Flows in PDEs -- 1 p-Laplace Equation, Heat Equation in Domains, Fokker-Planck Equation -- 2 The Heat Equation in Riemannian Manifolds -- 3 Dual Sobolev Space H-1 and Heat Flow in H-1 -- Lecture 14: Gradient Flows: The EDE and EDI Formulations -- 1 EDE, EDI Solutions and Upper Gradients -- 2 Existence of EDE, EDI Solutions -- 3 Proof of Theorem 14.7 via Variational Interpolation -- Lecture 15: Semicontinuity and Convexity of Energies in the Wasserstein Space -- 1 Semicontinuity of Internal Energies -- 2 Convexity of Internal Energies -- 3 Potential Energy Functional -- 4 Interaction Energy -- 5 Functional Inequalities via Optimal Transport -- Lecture 16: The Continuity Equation and the Hopf-Lax Semigroup -- 1 Continuity Equation and Transport Equation -- 2 Continuity Equation of Geodesics in the Wasserstein Space -- 3 Hopf-Lax Semigroup -- Lecture 17: The Benamou-Brenier Formula -- 1 Benamou-Brenier Formula -- 2 Correspondence Between Absolutely Continuous Curves in the Probabilities and Solutions to the Continuity Equation.Lecture 18: An Introduction to Otto's Calculus -- 1 Otto's Calculus -- 2 Formal Interpretation of Some Evolution Equations as Wasserstein Gradient Flows -- 3 Rigorous Interpretation of the Heat Equation as a Wasserstein Gradient Flow -- 4 More Recent Ideas and Developments -- Lecture 19: Heat Flow, Optimal Transport and Ricci Curvature -- 1 Heat Flow on Riemannian Manifolds -- 2 Heat Flow, Optimal Transport and Ricci Curvature -- References.Unitext Mathematical optimizationOptimització matemàticathubLlibres electrònicsthubMathematical optimization.Optimització matemàtica519.6Ambrosio Luigi44009Brué EliaSemola DanieleMiAaPQMiAaPQMiAaPQBOOK996466414703316Lectures on Optimal Transport2175022UNISA04272nam 2200661 450 991078907900332120230213215810.00-674-28160-810.4159/harvard.9780674281608(CKB)3390000000059613(SSID)ssj0001123192(PQKBManifestationID)11732270(PQKBTitleCode)TC0001123192(PQKBWorkID)11071763(PQKB)10390537(MiAaPQ)EBC3046288(DE-B1597)247936(OCoLC)1013954716(OCoLC)1029811428(OCoLC)1032684512(OCoLC)1037983071(OCoLC)1042027490(OCoLC)1046619076(OCoLC)1047022911(OCoLC)1049677564(OCoLC)1054880718(OCoLC)979740096(DE-B1597)9780674281608(Au-PeEL)EBL3046288(CaPaEBR)ebr10970728(OCoLC)900564672(EXLCZ)99339000000005961320150215h19631963 uy 0engurcnu||||||||txtccrJohn Gorham Palfrey and the New England conscience /Frank Otto GatellReprint 2014Cambridge, Massachusetts :Harvard University Press,1963.©19631 online resource (353 pages) illustrations, portraitsIncludes index.0-674-28159-4 Front matter --Preface --Contents --Illustrations --I The Child --II The Student --III Liberal Theology --IV Brattle Street --V Dean Palfrey --VI The North American --VII The State House --VIII A Practicing Abolitionist --IX Conscience and Judgment --X "He Knows Nothing About Politicks" --XI Down with Old Zack --XII Trial by Stalemate --XIII Defeat --XIV Political Twilight and the Puritan Past --XV War Against the Slave Power --XVI The Celebrated New Englander --Manuscript Collections Cited. Palfrey's Books and Pamphlets. Notes. Index --Manuscript Collections Cited --Palfrey's Books and Pamphlets --Notes --IndexThe New England of his day regarded John Gorham Palfrey's life as blameless and exemplary, a nineteenth-century "monument to the Puritan ideal of rectitude." Yet he himself once called it "his personal tragicomedy." At least, it was diverse, for Palfrey had been historian, Harvard educator, Unitarian minister, Massachusetts politician, editor of the North American Review, and crusader against slavery, and himself an emancipator. During his lifetime, from 1796 to 1881, Palfrey participated, sometimes reluctantly, in revolutionary changes in the political, economic, and intellectual climate of New England. In his stormy political career, Palfrey not only was Massachusetts Secretary of State, member of Congress, and Postmaster of Boston, but also played a key role in the formation of the Free Soil Party. When the Whigs, in the name of national unity and compromise, seemed to ignore the moral necessities of the slavery question, he joined with such men as Charles Francis Adams, Charles Sumner and Richard Henry Dana, Jr., to reaffirm traditional moral values. From this struggle, Palfrey emerged a political loser. Hampered by inflexibility, he later retreated to his study to write his massive history of New England, nursing his disappointment and cherishing his sense of rectitude. We are left with the image of a man whose achievements were substantial, perhaps because he insisted upon making his life a Bay State morality play. For this biography of Palfrey, Gatell has used papers of Palfrey's contemporaries and of the Palfrey family manuscripts, among them an unpublished autobiography, itself a search for meaning in a long and perplexing life.BIOGRAPHY & AUTOBIOGRAPHY / PoliticalbisacshBIOGRAPHY & AUTOBIOGRAPHY / Political.923.273Gatell Frank Otto464917MiAaPQMiAaPQMiAaPQBOOK9910789079003321John Gorham Palfrey and the New England conscience3686794UNINA