ERROR BOUNDS FOR CONVEX POLYNOMIALS

作者：Yang W H^*

来源：SIAM Journal on Optimization, 2009, 19(4): 1633-1647.

DOI：10.1137/070689838

• error bound
• convex polynomial
• kernel
• recession cone

The purpose of this paper is to investigate error bounds for convex polynomials. We prove that for a convex polynomial f in n variables which is not everywhere positive and which is not constant on any affine subspace, either f is a sum of a convex polynomial in fewer variables and a linear form with negative coefficients or the negativity set of f is compact. As an application, we deduce various types of error bounds for unconstrained and polyhedral-constrained convex polynomials.

• 出版日期2009
• 单位复旦大学