Global Optimization with Polynomials and the Problem of Moments

Jean B. Lasserre

Type: Article

Publication Date: 2001-01-01

Citations: 2594

DOI: https://doi.org/10.1137/s1052623400366802

View Publication

Locations

SIAM Journal on Optimization - View

Similar Works

Action	Title	Year	Authors
+	Global optimization of mixed-integer nonlinear (polynomial) programming problems: the Bernstein polynomial approach	2011	Bhagyesh V. Patil P. S. V. Nataraj Sharad Bhartiya
+ PDF Chat	An Introduction to Polynomial and Semi-Algebraic Optimization	2015	Jean B. Lasserre
+ PDF Chat	Detecting Global Optimality and Extracting Solutions in GloptiPoly	2005	Didier Henrion Jean B. Lasserre
+ PDF Chat	Solving Global Optimization Problems over Polynomials with GloptiPoly 2.1	2003	Didier Henrion Jean B. Lasserre
+ PDF Chat	None	2003	René Meziat
+	Global Optimization with Polynomials	2004	Deren Han
+	Analysis of Non Convex Polynomial Programs by the Method of Moments	2004	René Meziat
+ PDF Chat	GloptiPoly: global optimization over polynomials with Matlab and SeDuMi	2003	Didier Henrion Jean B. Lasserre
+	GpoSolver: a Matlab/C++ toolbox for global polynomial optimization	2016	Jan Heller Tomáš Pajdla
+	Global optimality conditions and optimization methods for polynomial programming problems and their applications	2014	Jing Tian
+	Robust global optimization with polynomials	2005	Jean B. Lasserre
+	Contributions to the moment-SOS approach in global polynomial optimization	2012	Thanh Tung Phan
+	A Method for Estimating the Bounds of a Real Valued Polynomial's Global Minimizers	2008	Jingying Ma
+ PDF Chat	Convergent Relaxations of Polynomial Matrix Inequalities and Static Output Feedback	2006	Didier Henrion Jean B. Lasserre
+	GloptiPoly	2003	Didier Henrion Jean B. Lasserre
+	THE MOMENT-SOS HIERARCHY	2019	Jean B. Lasserre
+	Global optimization of nonconvex generalized polynomial design models.	1991	Chihsiung Lo
+ PDF Chat	Moments matrices, real algebraic geometry and polynomial optimization	2014	Marta Abril Bucero
+	Chapter 13: Positivity of Polynomials and Global Optimization	2012
+	The approach of moments for polynomial equations	2012	Monique Laurent Philipp Rostalski

Works That Cite This (1912)

Action	Title	Year	Authors
+	多項式計画と錐線形計画 : 非線形計画への線形計画からのアプローチ( 堅く柔らかく…数理計画アプローチ再訪)	2006	村松正和
+	A geometric approach to exactness of Lasserre's relaxation	2021	Zheng Hua Zheng Qu
+	Global Uniqueness and Solvability of Tensor Variational Inequalities	2018	Yong Wang Zheng‐Hai Huang Liqun Qi
+ PDF Chat	A Finite Algorithm to Compute Rank-1 Tensor Approximations	2016	Alex P. da Silva Pierre Comon André L. F. de Almeida
+ PDF Chat	A new full-Newton step O(n) infeasible interior-point algorithm for semidefinite optimization	2009	H. Mansouri C. Roos
+ PDF Chat	Symmetric Tensor Nuclear Norms	2017	Jiawang Nie
+ PDF Chat	Exploiting term sparsity in noncommutative polynomial optimization	2021	Jie Wang Victor Magron
+ PDF Chat	Controller design and value function approximation for nonlinear dynamical systems	2016	Milan Korda Didier Henrion Colin N. Jones
+ PDF Chat	Bilevel Polynomial Programs and Semidefinite Relaxation Methods	2017	Jiawang Nie Li Wang Jane J. Ye
+ PDF Chat	Solving Fractional Polynomial Problems by Polynomial Optimization Theory	2018	Andrea Pizzo Alessio Zappone Luca Sanguinetti

Works Cited by This (12)

Action	Title	Year	Authors
+	Moments in Mathematics	1987	Henry Landau
+	A Collection of Test Problems for Constrained Global Optimization Algorithms	1990	Christodoulos A. Floudas Pãnos M. Pardalos
+	Hilbert’s 17th problem and best dual bounds in quadratic minimization	1998	Ch. Ferrier
+	The Classical Moment Problem as a Self-Adjoint Finite Difference Operator	1998	Barry Simon
+	Nondifferentiable Optimization and Polynomial Problems	1998	N. Z. Shor
+	A representation theorem for certain partially ordered commutative rings	2001	Thomas Jacobi
+ PDF Chat	Solving Moment Problems by Dimensional Extension	1999	Mihai Putinar Florian-Horia Vasilescu
+ PDF Chat	Lagrangian stability and global optimality in nonconvex quadratic minimization over Euclidean balls and spheres	1995	Tao Pham Dinh Hoai An Le Thi
+	Semidefinite Programming	1996	Lieven Vandenberghe Stephen Boyd
+	Squared functional systems and optimization problems	2000	Yu. Nesterov