alphaBB: A Global Optimization Method for General Constrained Nonconvex Problems

. A branch and bound global optimization method, ffBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convexrelaxation of the original nonconvexproblem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the ff parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finite ffl--convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method, ffBB, is implemented in C and tested on a variety of example problems. Keywords: Global optimization, constrained optimization, con..

Characterizing zero-derivative points

Zero-derivative point, Fermat’s extreme value theorem, Theorem of Lagrange, 26B05, 90C30,