An algorithm for solving convex programs with an additional convex-concave constraint

An implementable decomposition method based on branch-and-bound techniques is proposed for finding a global optimal solution of certain convex programs with an additional convex-concave constraint h(x,y)•0. A nonadaptive simplicial and an adaptive bisection are used for the branching operation, which is performed in y-space only. The bounding operation is based on a relaxation of the convex-concave constraint h(x,y)•0. The algorithm can be applied efficiently for linear programs with an additional affine multiplicative constraint.