Abstract：This paper studies global optimization for a class of sum for quadratic ratio problems by using a penalty function and a simplicial branch and a bound approach. Making use of the exponential function and linearizing method, the algorithm converts constraint optimization problems to nonconstraint optimization problems.Then, the algorithm is developed and the convergence of the algorithm is proposed through theoretical analysis.

Keyword：sum of quadratic ratios;penalty function;exponential function;simplicial branch and bound approach;global optimization;