An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Global Minimization of a Multivariate Polynomial using Matrix Methods
Journal of Global Optimization
Multivariate Polynomial Minimization and Its Application in Signal Processing
Journal of Global Optimization
On cones of nonnegative quadratic functions
Mathematics of Operations Research
Optimization of Polynomial Fractional Functions
Journal of Global Optimization
On the complexity of Schmüdgen's positivstellensatz
Journal of Complexity
Journal of Global Optimization
Minimum Ellipsoid Bounds for Solutions of Polynomial Systems via Sum of Squares
Journal of Global Optimization
A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem
Computational Optimization and Applications
Complete Solutions and Extremality Criteria to Polynomial Optimization Problems
Journal of Global Optimization
Efficiency improvement in an nD systems approach to polynomial optimization
Journal of Symbolic Computation
On the complexity of Putinar's Positivstellensatz
Journal of Complexity
Computation of the Lasserre Ranks of Some Polytopes
Mathematics of Operations Research
A conversion of an SDP having free variables into the standard form SDP
Computational Optimization and Applications
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Annals of Mathematics and Artificial Intelligence
A note on the stability number of an orthogonality graph
European Journal of Combinatorics
Numerical optimization in hybrid symbolic-numeric computation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Lower bounds for approximate factorizations via semidefinite programming: (extended abstract)
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Approximate GCDs of polynomials and SOS relaxation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
An alternative approach for non-linear optimal control problems based on the method of moments
Computational Optimization and Applications
A geometric approach to monitoring threshold functions over distributed data streams
ACM Transactions on Database Systems (TODS)
Automatica (Journal of IFAC)
Global optimization for sum of generalized fractional functions
Journal of Computational and Applied Mathematics
Simulation of discrete linear time-invariant fuzzy dynamic systems
Fuzzy Sets and Systems
Global minimization of rational functions and the nearest GCDs
Journal of Global Optimization
Transitivity and topological entropy on fuzzy dynamical systems through fuzzy observation
FS'07 Proceedings of the 8th Conference on 8th WSEAS International Conference on Fuzzy Systems - Volume 8
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Revisiting stochastic loss networks: structures and algorithms
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
ACM Transactions on Mathematical Software (TOMS)
Computing the global optimum of a multivariate polynomial over the reals
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Automatica (Journal of IFAC)
On the Kalman---Yakubovich---Popov lemma and the multidimensional models
Multidimensional Systems and Signal Processing
Approximate GCDs of polynomials and sparse SOS relaxations
Theoretical Computer Science
Computing sum of squares decompositions with rational coefficients
Theoretical Computer Science
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones
Computational Optimization and Applications
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
Brief paper: An alternative Kalman-Yakubovich-Popov lemma and some extensions
Automatica (Journal of IFAC)
Sum of squares method for sensor network localization
Computational Optimization and Applications
Automatica (Journal of IFAC)
Proceedings of the 2009 conference on Symbolic numeric computation
A p-cone sequential relaxation procedure for 0-1 integer programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
GloptiPoly 3: moments, optimization and semidefinite programming
Optimization Methods & Software - GLOBAL OPTIMIZATION
Moments and sums of squares for polynomial optimization and related problems
Journal of Global Optimization
Solving polynomial least squares problems via semidefinite programming relaxations
Journal of Global Optimization
Convex relaxations in circuits, systems, and control
IEEE Circuits and Systems Magazine
Linearized analysis versus optimization-based nonlinear analysis for nonlinear systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
Exploiting sparsity in the sum-of-squares approximations to robust semidefinite programs
ACC'09 Proceedings of the 2009 conference on American Control Conference
Parameter-dependent Slack variable approach for positivity check of polynomials over hyper-rectangle
ACC'09 Proceedings of the 2009 conference on American Control Conference
Group search optimizer: an optimization algorithm inspired by animal searching behavior
IEEE Transactions on Evolutionary Computation
A robust SDP approach to system identification with roughly quantized data
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
A Heuristic for Nonlinear Global Optimization
INFORMS Journal on Computing
Optimization of structured mean field objectives
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Robust stabilisation of polynomial systems with uncertain parameters
International Journal of Systems Science
Optimal linear-consensus algorithms: an LQR perspective
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
$${{\mathcal {D}(\mathcal {C})}}$$-optimization and robust global optimization
Journal of Global Optimization
Optimal non-iterative pose estimation via convex relaxation
Image and Vision Computing
Global optimization of polynomials using generalized critical values and sums of squares
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Brief paper: Convex relaxations for mixed integer predictive control
Automatica (Journal of IFAC)
Globally Optimal Algorithms for Stratified Autocalibration
International Journal of Computer Vision
Partitioning procedure for polynomial optimization
Journal of Global Optimization
Breaking the rectangle bound barrier against formula size lower bounds
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Exploiting structured sparsity in large scale semidefinite programming problems
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Removing redundant quadratic constraints
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Beyond convexity: new perspectives in computational optimization
SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
SIAM Journal on Optimization
A “Joint+Marginal” Approach to Parametric Polynomial Optimization
SIAM Journal on Optimization
Theta Bodies for Polynomial Ideals
SIAM Journal on Optimization
A Variational Approach to Copositive Matrices
SIAM Review
Convergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables
SIAM Journal on Optimization
Towards the geometry of estimation of distribution algorithms based on the exponential family
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Neural networks and genetic algorithms for robust predictive controller
ACMOS'06 Proceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation
Original article: The domain of attraction for the endemic equilibrium of an SIRS epidemic model
Mathematics and Computers in Simulation
Computational complexity of the quantum separability problem
Quantum Information & Computation
An iterative scheme for valid polynomial inequality generation in binary polynomial programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Integrality gaps of linear and semi-definite programming relaxations for Knapsack
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Security proof of quantum key distribution with detection efficiency mismatch
Quantum Information & Computation
Computing time-dependent policies for patrolling games with mobile targets
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Min-max and robust polynomial optimization
Journal of Global Optimization
Automatica (Journal of IFAC)
Discriminants and nonnegative polynomials
Journal of Symbolic Computation
Representations of Positive Polynomials and Optimization on Noncompact Semialgebraic Sets
SIAM Journal on Optimization
SIAM Journal on Optimization
Positivity and Optimization for Semi-Algebraic Functions
SIAM Journal on Optimization
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
International Journal of Automation and Computing
Sherali-Adams relaxations and indistinguishability in counting logics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Convergent SDP-relaxations for polynomial optimization with sparsity
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Semidefinite bounds for the stability number of a graph via sums of squares of polynomials
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Global optimization of polynomials restricted to a smooth variety using sums of squares
Journal of Symbolic Computation
Journal of Global Optimization
Hypercontractivity, sum-of-squares proofs, and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Ellipsoidal bounds for uncertain linear equations and dynamical systems
Automatica (Journal of IFAC)
Uniform stabilization of discrete-time switched and Markovian jump linear systems
Automatica (Journal of IFAC)
A facial reduction algorithm for finding sparse SOS representations
Operations Research Letters
Stochastic 0-1 linear programming under limited distributional information
Operations Research Letters
Approximating integrals of multivariate exponentials: A moment approach
Operations Research Letters
Inverse conic programming with applications
Operations Research Letters
Computational Optimization and Applications
Maximum Block Improvement and Polynomial Optimization
SIAM Journal on Optimization
Bounded error identification of Hammerstein systems through sparse polynomial optimization
Automatica (Journal of IFAC)
ACM Transactions on Mathematical Software (TOMS)
Computation of polytopic invariants for polynomial dynamical systems using linear programming
Automatica (Journal of IFAC)
Reachability analysis of polynomial systems using linear programming relaxations
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
On solving biquadratic optimization via semidefinite relaxation
Computational Optimization and Applications
Computational Optimization and Applications
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Computing real solutions of polynomial systems via low-rank moment matrix completion
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Minimizing ordered weighted averaging of rational functions with applications to continuous location
Computers and Operations Research
Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
Mathematics of Operations Research
0/1 polytopes with quadratic chvátal rank
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Theoretical Computer Science
Convex algebraic geometry and semidefinite optimization
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials
Computational Optimization and Applications
Lifts of Convex Sets and Cone Factorizations
Mathematics of Operations Research
Majority is stablest: discrete and SoS
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Quantum de finetti theorems under local measurements with applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares
Mathematics of Operations Research
Solution to singular optimal control by backward differential flow
Journal of Control Science and Engineering
Certification of bounds of non-linear functions: the templates method
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity
Journal of Global Optimization
Atomic optimization. I. Search Space Transformation and One-dimensional Problems
Automation and Remote Control
Journal of Global Optimization
An SDP approach for ℓ0-minimization: Application to ARX model segmentation
Automatica (Journal of IFAC)
Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities
Journal of Global Optimization
Lower bounds on the global minimum of a polynomial
Computational Optimization and Applications
Hi-index | 0.03 |
We consider the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): {\mathbb{R}}^n\to {\mathbb{R}}$, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush--Kuhn--Tucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided.