In this paper, we introduce a new cutting plane algorithm which is computationally less expensive and more efficient than Kelley's algorithm. This new cutting plane algorithm uses an intersection cut of three types of cutting planes. We find from numerical results that the global search method formed using successive linear programming and a new intersection set is at least twice as fast as Kelley's cutting planes. The necessary mathematical analysis and convergence theorem are provided. The key findings are illustrated via optimization of a cascade of three CSTRs. (C) 2010 Elsevier Ltd. All rights reserved.