Semidefinite programming and arithmetic circuit evaluation

@article{Tarasov2008SemidefinitePA,
  title={Semidefinite programming and arithmetic circuit evaluation},
  author={S. Tarasov and M. Vyalyi},
  journal={ArXiv},
  year={2008},
  volume={abs/cs/0512035}
}
  • S. Tarasov, M. Vyalyi
  • Published 2008
  • Computer Science, Mathematics
  • ArXiv
  • We address the exact semidefinite programming feasibility problem (SDFP) consisting in checking that intersection of the cone of positive semidefinite matrices and some affine subspace of matrices with rational entries is not empty. SDFP is a convex programming problem and is often considered as tractable since some of its approximate versions can be efficiently solved, e.g. by the ellipsoid algorithm. We prove that SDFP can decide comparison of numbers represented by the arithmetic circuits, i… CONTINUE READING
    13 Citations
    Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism Problem
    • 10
    • PDF
    On the computing power of +, -, and ×
    • M. Mamino
    • Mathematics, Computer Science
    • CSL-LICS
    • 2014
    • 1
    Algorithms in Real Algebraic Geometry: A Survey
    • S. Basu
    • Computer Science, Mathematics
    • ArXiv
    • 2014
    • 24
    • PDF
    A Semidefinite Programming Approach for Harmonic Balance Method
    • 1
    Constraint Satisfaction Problems over Numeric Domains
    • 9
    • PDF
    Projections onto the Set of Feasible Inputs and the Set of Feasible Solutions
    • 1
    • PDF
    SOS Is Not Obviously Automatizable, Even Approximately
    • 32
    • PDF
    On the Computing Power of $+$, $-$, and $\times$
    • 1
    • PDF
    On the complexity of numerical analysis
    • 154
    • PDF

    References

    SHOWING 1-10 OF 35 REFERENCES
    On the Complexity of Semidefinite Programs
    • 83
    An exact duality theory for semidefinite programming and its complexity implications
    • 218
    Handbook of Semidefinite Programming
    • 672
    • PDF
    Geometric Algorithms and Combinatorial Optimization
    • 2,752
    A new polynomial-time algorithm for linear programming
    • 3,545
    The complexity of combinatorial problems with succinct input representation
    • K. Wagner
    • Mathematics, Computer Science
    • Acta Informatica
    • 2004
    • 153
    Complexity and Real Computation
    • L. Blum
    • Mathematics, Computer Science
    • Springer New York
    • 1998
    • 1,414
    • PDF
    Completeness classes in algebra
    • 509
    Valiant’s model and the cost of computing integers
    • P. Koiran
    • Mathematics, Computer Science
    • computational complexity
    • 2004
    • 32
    • PDF