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Global Optimization with Polynomials and the Problem of Moments
TLDR
It is shown that the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): R n to R, in a compact set K defined byPolynomial inequalities reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems.
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Moments, Positive Polynomials And Their Applications
TLDR
The semidefinite programming methodology to solve the generalized problem of moments is presented and several applications of the GPM are described in detail (notably in optimization, probability, optimal control andmathematical finance).
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Further topics on discrete-time Markov control processes
7 Ergodicity and Poisson's Equation.- 7.1 Introduction.- 7.2 Weighted norms and signed kernels.- A. Weighted-norm spaces.- B. Signed kernels.- C. Contraction maps.- 7.3 Recurrence concepts.- A.…
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Discrete-time Markov control processes
1 Introduction and Summary.- 1.1 Introduction.- 1.2 Markov control processes.- 1.3 Preliminary examples.- 1.4 Summary of the following chapters.- 2 Markov Control Processes.- 2.1 Introduction.- 2.2…
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GloptiPoly: global optimization over polynomials with Matlab and SeDuMi
GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally non-convex) global optimization problem of minimizing a multivariable polynomial…
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GloptiPoly 3: moments, optimization and semidefinite programming
TLDR
A major update of the Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming is described.
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An Introduction to Polynomial and Semi-Algebraic Optimization
This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic…
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Detecting global optimality and extracting solutions in GloptiPoly
GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality (LMI) relaxations of non-convex optimization problems with multivariate polynomial objective function and…
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An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
TLDR
This work considers the general nonlinear optimization problem in 0-1 variables and provides an explicit equivalent positive semidefinite program in 2n-1 variable and its optimal values are identical.
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SIAM Journal on Optimization
The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear…
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