Mathematics of Operations Research
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
On Tractable Approximations of Uncertain Linear Matrix Inequalities Affected by Interval Uncertainty
SIAM Journal on Optimization
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness
SIAM Journal on Matrix Analysis and Applications
The Rectilinear Steiner Arborescence Problem Is NP-Complete
SIAM Journal on Computing
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity
SIAM Journal on Optimization
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This paper aims to improve computational complexity in the sum-of-squares approximations to robust semidefinite programs whose constraints depend polynomially on uncertain parameters. By exploiting sparsity, the proposed approach constructs sum-of-squares polynomials with smaller number of monomial elements, and hence gives approximate problems with smaller sizes. The sparse structure is extracted by a special graph pattern. The quality of the approximation is improved by dividing the parameter region, and can be expressed in terms of the resolution of the division. This expression shows that the proposed approach is asymptotically exact in the sense that, the quality can be arbitrarily improved by increasing the resolution of the division.