GloptiPoly 3: moments, optimization and semidefinite programming
TLDR
The authors describe a major update of GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming, which is based on the Matlab freeware GlopiPoly.Abstract:
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming.read more
Citations
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Book ChapterDOI
Sums of Squares, Moment Matrices and Optimization Over Polynomials
TL;DR: This work considers the problem of minimizing a polynomial over a semialgebraic set defined byPolynomial equations and inequalities, which is NP-hard in general and reviews the mathematical tools underlying these properties.
Journal ArticleDOI
Non-convex mixed-integer nonlinear programming: A survey
Samuel Burer,Adam N. Letchford +1 more
TL;DR: In this paper, the authors survey the literature on non-convex mixed-integer nonlinear programs, discussing applications, algorithms, and software, and special attention is paid to the case in which the objective and constraint functions are quadratic.
Journal ArticleDOI
Convex Computation of the Region of Attraction of Polynomial Control Systems
Didier Henrion,Milan Korda +1 more
TL;DR: The ROA can be computed by solving a convex linear programming (LP) problem over the space of measures and this problem can be solved approximately via a classical converging hierarchy of convex finite-dimensional linear matrix inequalities (LMIs).
Book
An Introduction to Polynomial and Semi-Algebraic Optimization
TL;DR: In this paper, a comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions) is presented.
Book ChapterDOI
On the Implementation and Usage of SDPT3 – A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0
TL;DR: Numerical experiments show that this general-purpose code can solve more than 80% of a total of about 430 test problems to an accuracy of at least 10 − 6 in relative duality gap and infeasibilities.
References
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Proceedings ArticleDOI
YALMIP : a toolbox for modeling and optimization in MATLAB
TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.
Journal ArticleDOI
Global Optimization with Polynomials and the Problem of Moments
TL;DR: 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.
Book ChapterDOI
Sums of Squares, Moment Matrices and Optimization Over Polynomials
TL;DR: This work considers the problem of minimizing a polynomial over a semialgebraic set defined byPolynomial equations and inequalities, which is NP-hard in general and reviews the mathematical tools underlying these properties.
Journal ArticleDOI
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
Didier Henrion,Jean B. Lasserre +1 more
TL;DR: GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally nonconvex) global optimization problem of minimizing a multivariable polynomial function subject to polynometric inequality, equality, or integer constraints.