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Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.

Integer programming. --- Mathematical optimization. --- Nonlinear programming. --- Nonlinear programming --- Integer programming --- Mathematical optimization --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mathematics. --- Approximation theory. --- Algorithms. --- Approximations and Expansions. --- Continuous Optimization. --- Programming (Mathematics) --- Math --- Science --- Algorism --- Algebra --- Arithmetic --- Foundations --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on "ients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.

Mumford-Tate groups. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Hodge theory --- Mumford-Tate groups --- Deligne torus integer. --- Galois group. --- Grothendieck conjecture. --- Hodge decomposition. --- Hodge domain. --- Hodge filtration. --- Hodge orientation. --- Hodge representation. --- Hodge structure. --- Hodge tensor. --- Hodge theory. --- Kubota rank. --- Lie algebra representation. --- Lie group. --- Mumford-Tate domain. --- Mumford-Tate group. --- Mumford-Tate subdomain. --- Noether-Lefschetz locus. --- Vogan diagram method. --- Weyl group. --- abelian variety. --- absolute Hodge class. --- algebraic geometry. --- arithmetic group. --- automorphic cohomology. --- classical group. --- compact dual. --- complex manifold. --- complex multiplication Hodge structure. --- complex multiplication. --- endomorphism algebra. --- exceptional group. --- holomorphic mapping. --- homogeneous complex manifold. --- homomorphism. --- mixed Hodge structure. --- moduli space. --- monodromy group. --- natural symmetry group. --- oriented imaginary number fields. --- period domain. --- period map. --- polarization. --- polarized Hodge structure. --- pure Hodge structure. --- reflex field. --- semisimple Lie algebra. --- semisimple Lie group. --- Γ-equivalence classes.