alphaBB swMATH ID: 6249 Software Authors: I.P. Androulakis , C.D. Maranas , C.A. FLOUDAS Description: 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. Homepage: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.3684 Related Software: CPLEX; SNOPT; BARON; INTOPT_90; GAMS; Matlab; SeDuMi; LaGO; AlphaECP; Optimization Toolbox; GLOPEQ; RLT-POS; Couenne; SparsePOP; NEOS; MacMPEC; KNITRO; Boost Interval Arithmetic; Boost; GGPECP Cited in: 49 Publications all top 5 Cited by 80 Authors 17 Floudas, Christodoulos Achilleus 3 Barton, Paul I. 3 Klepeis, John L. 3 Liberti, Leo 3 Pardalos, Panos M. 2 Akrotirianakis, Ioannis G. 2 Fung, Ho Ki 2 Kreinovich, Vladik Yakovlevich 2 Meyer, Clifford A. 2 Nowak, Ivo 2 Singer, Adam B. 2 Stein, Oliver 2 Westerlund, Tapio 1 Adjiman, Claire S. 1 Allgor, Russell J. 1 Androulakis, Ioannis P. 1 Birgin, Ernesto G. 1 Bompadre, Agustín 1 Bueno, Luís Felipe 1 Castillo, Ignacio 1 Castro, Pedro M. 1 Chachuat, Benoît 1 Chen, Xi 1 Dalkiran, Evrim 1 Dhyani, Kanika 1 Domes, Ferenc 1 Gatzke, Edward P. 1 Gjerdrum, Jonatan 1 Gounaris, Chrysanthos E. 1 Gümüş, Zeynep H. 1 Ho, Ka-Leung 1 Ho, Yuen-Hong Alvin 1 Hou, Xiaorong 1 Jach, Matthias 1 Kallrath, Josef 1 Kesavan, Padmanaban 1 Klimke, W. Andreas 1 Krejić, Nataša 1 Kwan, Hing-Kit 1 Latifi, M. A. 1 Lee, Cha Kun 1 Lee, Yu-Ching 1 Li, Zhaohua 1 Lundell, Andreas 1 Martínez, José Mario 1 Matos, Henrique A. 1 Michaels, Dennis 1 Misener, Ruth 1 Mitchell, John E. 1 Mitsos, Alexander 1 Neumaier, Arnold 1 O’brien, Liam M. 1 Pang, Jong-Shi 1 Papageorgiou, Lazaros G. 1 Papamichail, Ioannis 1 Pieja, M. J. 1 Price, Christopher John 1 Prokopyev, Oleg Alexan 1 Rendl, Franz 1 Robertson, B. L. 1 Romeijn, H. Edwin 1 Shah, Nilay 1 Shang, Youlin 1 Shao, Junwei 1 Shao, Zhijiang 1 Sherali, Hanif D. 1 Skjäl, Anders 1 Stolpe, Mathias 1 Szeto, Wai Yuen 1 Taylor, Martin S. 1 Teles, João P. 1 Tian, Daqing 1 Tuy, Hoang 1 Vigerske, Stefan 1 Weismantel, Robert 1 Westerberg, K. M. 1 Winterfeld, Anton 1 Wolfe, Michael A. 1 Wu, Dan 1 Yang, Jing all top 5 Cited in 24 Serials 13 Journal of Global Optimization 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational and Applied Mathematics 2 Mathematical Programming. Series A. Series B 2 SIAM Journal on Optimization 2 Optimization Methods & Software 1 Computer Physics Communications 1 International Journal of Circuit Theory and Applications 1 Journal of Optimization Theory and Applications 1 Systems & Control Letters 1 Computers & Operations Research 1 SIAM Journal on Matrix Analysis and Applications 1 European Journal of Operational Research 1 Linear Algebra and its Applications 1 Journal of Combinatorial Optimization 1 CEJOR. Central European Journal of Operations Research 1 RAIRO. Operations Research 1 Journal of Applied Mathematics 1 4OR 1 Computational Management Science 1 Networks and Spatial Economics 1 ISNM. International Series of Numerical Mathematics 1 Optimization Letters 1 Mathematical Programming Computation all top 5 Cited in 14 Fields 44 Operations research, mathematical programming (90-XX) 10 Numerical analysis (65-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Biology and other natural sciences (92-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year