A PTAS for the minimization of polynomials of fixed degree over the simplex
Theoretical Computer Science - Approximation and online algorithms
A linear programming reformulation of the standard quadratic optimization problem
Journal of Global Optimization
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
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
Journal of Global Optimization
Exploiting equalities in polynomial programming
Operations Research Letters
SIAM Journal on Optimization
Strong duality and minimal representations for cone optimization
Computational Optimization and Applications
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An interesting recent trend in optimization is the application of semidefinite programming techniques to new classes of optimization problems. In particular, this trend has been successful in showing that under suitable circumstances, polynomial optimization problems can be approximated via a sequence of semidefinite programs. Similar ideas apply to conic optimization over the cone of copositive matrices and to certain optimization problems involving random variables with some known moment information.We bring together several of these approximation results by studying the approximability of cones of positive semidefinite forms (homogeneous polynomials). Our approach enables us to extend the existing methodology to new approximation schemes. In particular, we derive a novel approximation to the cone of copositive forms, that is, the cone of forms that are positive semidefinite over the nonnegative orthant. The format of our construction can be extended to forms that are positive semidefinite over more general conic domains. We also construct polyhedral approximations to cones of positive semidefinite forms over a polyhedral domain. This opens the possibility of using linear programming technology in optimization problems over these cones.