GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem
Computational Optimization and Applications
A linear programming reformulation of the standard quadratic optimization problem
Journal of Global Optimization
Efficiency improvement in an nD systems approach to polynomial optimization
Journal of Symbolic Computation
Annals of Mathematics and Artificial Intelligence
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Theta Bodies for Polynomial Ideals
SIAM Journal on Optimization
Original article: The domain of attraction for the endemic equilibrium of an SIRS epidemic model
Mathematics and Computers in Simulation
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
SIAM Journal on Optimization
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
Convergent SDP-relaxations for polynomial optimization with sparsity
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Uniform stabilization of discrete-time switched and Markovian jump linear systems
Automatica (Journal of IFAC)
Exploiting equalities in polynomial programming
Operations Research Letters
Block-diagonal semidefinite programming hierarchies for 0/1 programming
Operations Research Letters
The equivalence of semidefinite relaxations of polynomial 0-1 and ±1 programs via scaling
Operations Research Letters
Computational Optimization and Applications
Approximating k-median via pseudo-approximation
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Cones of multipowers and combinatorial optimization problems
Computational Mathematics and Mathematical Physics
On integrality ratios for asymmetric TSP in the sherali-adams hierarchy
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Lift-and-Project methods for set cover and knapsack
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Semidefinite resolution and exactness of semidefinite relaxations for satisfiability
Discrete Applied Mathematics
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We consider the general nonlinear optimization problem in 0-1 variables and provide an explicit equivalent positive semidefinite program in 2n-1 variables. The optimal values of both problems are identical. From every optimal solution of the former, one easily finds an optimal solution of the latter, and conversely, from every solution of the latter, one may construct an optimal solution of the former. For illustration, the equivalent positive semidefinite program is explicated for quadratic 0-1 programs and MAX-CUT in $\mathbb{R}^3$. For unconstrained 0-1 programs, a special representation in terms of a weighted sum of squares is provided.