Theory of linear and integer programming
Theory of linear and integer programming
On the computational complexity of approximating solutions for real algebraic formulae
SIAM Journal on Computing
Mathematical Programming: Series A and B
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An Exact Duality Theory for Semidefinite Programming and its Complexity Implications
An Exact Duality Theory for Semidefinite Programming and its Complexity Implications
An algorithmic analysis of multiquadratic and semidefinite programming problems
An algorithmic analysis of multiquadratic and semidefinite programming problems
Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon
Journal of Global Optimization
Semidefinite programming and arithmetic circuit evaluation
Discrete Applied Mathematics
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model
Mathematics of Operations Research
Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions
SIAM Journal on Optimization
An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares
Mathematics of Operations Research
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We show that the feasibility of a system of m linear inequalities over the cone of symmetric positive semidefinite matrices of order n can be tested in mn^O(min{m,n^2}) arithmetic operations with ln^O(min{m,n^2})-bit numbers, where l is the maximum binary size of the input coefficients. We also show that any feasible system of dimension (m,n) has a solution X such that log||X|| ≤ ln^O(min{m,n^2}).