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Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriat

Moments method (Statistics) --- Polynomials. --- Algebra --- Method of moments (Statistics) --- Mathematical statistics --- Distribution (Probability theory) --- Geometry, Algebraic --- Mathematical optimization --- Moment problems (Mathematics) --- Polynomials --- Calculus, Operational --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algebraic geometry --- Geometry