Moderate Nonlinearity = Convexity + Quadratic Concavity

Masakazu Kojima

Moderately nonlinear programs can be reduced to a quadratic program having a linear objective function, concave quadratic inequality constraints and an additional convex constraint set. This observation makes it possible to extend successive convex relaxation methods, which were recently proposed by Kojima and Tun\c{c}el for nonconvex quadratic programs, to a wide class of nonlinear programs.

Research Report B-348, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8852, Japan, March 1999