[1]

A.M. Agogino and A.S. Almgren, “Techniques for integrating qualitative reasoning and symbolic computation in engineering optimization,”*Engineering Optimization* 12 (1987) 117–135.

[2]

F. Archetti and F. Schoen, “A survey on the global optimization problem: general theory and computational approaches,”*Annals of Operations Research* 1 (1984) 87–110.

[3]

B. Aspvall, M.F. Plass and R.E. Tarjan, “A linear-time algorithm for testing the truth of certain quantified Boolean formulas,”*Information Processing Letters* 8 (1979) 121–123.

[4]

M. Avriel and A.C. Williams, “An extension of geometric programming with applications in engineering optimization,”*Journal of Engineering Mathematics* 5 (1971) 187–194.

[5]

E.M.L. Beale and J.J.H. Forrest, “Global optimization using special ordered sets,”*Mathematical Programming* 10 (1976) 52–69.

[6]

E.M.L. Beale and J.J.H. Forrest, “Global optimization as an extension of integer programming,” in: [16] pp. 131–150.

[7]

D.P. Bertsekas,*Constrained Optimization and Lagrange Multiplier Methods* (Academic Press, New York, 1982).

[8]

A.H. Boas, “Optimization via linear and dynamic programming,”*Chemical Engineering* 70 (1963) 85–88.

[9]

Y. Cherruault and A. Guillez, “Une méthode pour la recherche du minimum global d'une fonctionnelle,”*Comptes-Rendus de l'Académie des Sciences de Paris* 296 (1983) 175–179.

[10]

S.H. Chew and Q. Zheng,*Integral Global Optimization. Lecture Notes in Economics and Mathematical Systems No. 298* (Springer, New York, 1988).

[11]

F. Cole, “Some algorithms for geometric programming,” Ph.D. Thesis, Department of Applied Economics, University of Leuven (Leuven, Belgium, 1985).

[12]

A.R. Colville, “A comparative study of nonlinear programming codes,” IBM Scientific Report 320-2940 (New York, 1968).

[13]

A. Corana, M. Marchesi, C. Martini and S. Ridella, “Minimizing multimodal functions of continuous variables with the ‘Simulated Annealing’ algorithm,”*ACM Transactions on Mathematical Software* 13 (1987) 262–280.

[14]

H. Cornelius and R. Lohner, “Computing the range of real functions with accuracy higher than second order,”*Computing* 33 (1984) 331–347.

[15]

R.S. Dembo, “A set of geometric programming test problems and their solutions,”*Mathematical Programming* 10(2) (1976) 192–213.

[16]

L.C.W. Dixon and G.P. Szëgo, eds.,*Towards Global Optimization, Vol. 2* (North-Holland, Amsterdam, 1977).

[17]

A. Groch, L.M. Vidigal and S.W. Director, “A new global optimization method for electronic circuit design,”*IEEE Transactions on Circuits and Systems* CAS-32 (1985) 160–170.

[18]

Y. Fujii, K. Ichida and M. Ozasa, “Maximization of multivariate functions using interval analysis,” in: K. Nickel, ed.,*Interval Mathematics. Lecture Notes in Computer Science No. 212* (Springer, New York, 1985) pp. 37–56.

[19]

C.B. Garcia and W.I. Zangwill,*Pathways to Solutions, Fixed Points, and Equilibria. Series in Computational Mathematics* (Prentice-Hall, Englewood Cliffs, NJ, 1981).

[20]

C.R. Hammond and G.E. Johnson, “A general approach to constrained optimal design based on symbolic mathematics,” in: S.S. Rao, ed.,*Advances in Design Automation, Vol. 1: Design Methods, Computer Graphics and Expert Systems* (ASME, New York, 1987) pp. 31–40.

[21]

E. Hansen, “Global optimization using interval analysis—the multi dimensional case,”*Numerische Mathematik* 34 (1980) 247–270.

[22]

E. Hansen and S. Sengupta, “Global constrained optimization using interval analysis,” in: K.L.E. Nickel, ed.,*Interval Mathematics 1980* (Academic Press, New York, 1980) pp. 25–47.

[23]

P. Hansen, “Programmes mathématiques en variables 0–1,” Thèse d'agrégation, Université libre de Bruxelles (Bruxelles, 1974).

[24]

P. Hansen, “Les procédures d'optimisation et d'exploration par séparation et évaluation,” in: B. Roy, ed.,*Combinatorial Programming* (Reidel, Dordrecht, 1975) pp. 19–65.

[25]

P. Hansen, B. Jaumard and S.H. Lu, “Some further results on monotonicity analysis in globally optimal design,”*ASME, Journal of Mechanisms, Transmissions, and Automation in Design* 111 (1989) 345–352.

[26]

P. Hansen, B. Jaumard and S.H. Lu, “A framework for algorithms in globally optimal design,”*ASME, Journal of Mechanisms, Transmissions, and Automation in Design* 111 (1989) 353–360.

[27]

P. Hansen, B. Jaumard and M. Minoux, “A linear expected-time algorithm for deriving all logical conclusions implied by a set of Boolean inequalities,”*Mathematical Programming* 34 (1986) 223–231.

[28]

D.M. Himmelblau,*Applied Nonlinear Programming* (McGraw-Hill, New York, 1972).

[29]

W. Hock and K. Schittkowski,*Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems No. 18* (Springer, Heidelberg, 1981).

[30]

R. Horst, “A general class of branch-and-bound methods in global optimization with some new approaches for concave minimization,”*Journal of Optimization Theory and Applications* 51 (1986) 271–291.

[31]

R. Horst, “Deterministic global optimization with partition sets whose feasibility is not known: application to concave minimization, reverse convex constraints, d.c. programming, and Lipschitzian optimization,”*Journal of Optimization Theory and Applications* 58 (1988) 11–37.

[32]

R. Horst and N.V. Thoai, “Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems,”*Computing* 42 (1989) 271–289.

[33]

R. Horst, N.V. Thoai and H.P. Benson, “Concave minimization via conical partitions and polyhedral outer approximation,”*Mathematical Programming* 50 (1991) 259–274.

[34]

R. Horst and H. Tuy, “On the convergence of global methods in multiextremal optimization,”*Journal of Optimization Theory and Applications* 54 (1987) 253–271.

[35]

R. Horst, J. de Vries and N.V. Thoai, “On finding new vertices and redundant constraints in cutting-plane algorithms for global optimization,”*Operations Research Letters* 7 (1988) 85–90.

[36]

R.C. Johnson,*Optimum Design of Mechanical Elements* (Wiley, New York, 1980, 2nd ed.).

[37]

B. Kalantari and J.B. Rosen, “An algorithm for global minimization of linearly constrained concave quadratic functions,”*Mathematics of Operations Research* 12 (1987) 544–561.

[38]

A.V. Levy and A. Montalvo, “The tunneling algorithm for the global minimization of functions,”*SIAM Journal on Scientific and Statistical Computing* 6 (1985) 15–29.

[39]

R. Luus and T.H.I. Jaakola, “Optimization by direct search and systematic reduction of the size of search region,”*AIChE Journal* 19 (1973) 760–766.

[40]

G.P. McCormick,*Nonlinear Programming* (Wiley, New York, 1983).

[41]

C.C. Meewella and D.Q. Mayne, “An algorithm for global optimization of Lipschitz functions,”*Journal of Optimization Theory and Applications* 57 (1988) 307–323.

[42]

R.H. Mladineo, “An algorithm for finding the global maximum of a multimodal multivariate function,”*Mathematical Programming* 34 (1986) 188–200.

[43]

R.E. Moore,*Interval Analysis* (Prentice-Hall, Englewood Cliffs, NJ, 1966).

[44]

R.E. Moore,*Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics* (SIAM, Philadelphia, PA, 1979).

[45]

R.E. Moore and H. Ratschek, “Inclusion functions and global optimization II,”*Mathematical Programming* 41 (1988) 341–356.

[46]

A. Morgan,*Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems* (Prentice-Hall, Englewood Cliffs, NJ, 1987).

[47]

K.G. Murty and S.N. Kabadi, “Some NP-complete problems in quadratic and nonlinear programming,”*Mathematical Programming* 39 (1987) 117–130.

[48]

P.Y. Papalambros and H.L. Li, “Notes on the operational utility of monotonicity in optimization,”*ASME Journal of Mechanisms, Transmissions, and Automation in Design* 105 (1983) 174–180.

[49]

P.Y. Papalambros and D.J. Wilde,*Principles of Optimal Design: Modeling and Computation* (Cambridge University Press, Cambridge, 1988).

[50]

P. Pardalos and J. Rosen,*Constrained Global Optimization: Algorithms and Applications. Lecture Notes in Computer Science No. 268* (Springer, Berlin, 1988).

[51]

J. Pintér, “Branch-and-bound algorithms for solving global optimization problems with Lipschitzian structure,”*Optimization* 19 (1988) 101–110.

[52]

S.A. Piyavskii, “An algorithm for finding the absolute extremum of a function,”*USSR Computational Mathematics and Mathematical Physics* 12 (1972) 57–67. [*Zh. vychisl Mat. mat. Fiz.* 12 (1972) 888–896.]

[53]

W.V. Quine, “A Way to Simplify Truth Functions,”*American Mathematical Monthly* 62 (1955) 627–631.

[54]

G.S. Rao, R.S. Tyagi and R.K. Mishra, “Calculation of the minimum energy conformation of biomolecules using a global optimization technique. I. Methodology and application to a model molecular fragment (normal pentane),”*Journal of Theoretical Biology* 90 (1981) 377–389.

[55]

H. Ratschek and J. Rokne,*Computer Methods for the Range of Functions. Ellis Horwood Series in Mathematics and its Applications* (Halsted, New York, 1984).

[56]

H. Ratschek and J. Rokne,*New Computer Methods for Global Optimization. Ellis Horwood Series in Mathematics and its Applications* (Halsted, New York, 1988).

[57]

A.H.G. Rinnooy Kan and G.T. Timmer, “A stochastic approach to global optimization,” in: P.T. Boggs, ed.,*Numerical Optimization 84* (SIAM, Philadelphia, PA, 1985) pp. 245–262.

[58]

A.H.G. Rinnooy Kan and G.T. Timmer, “Stochastic global optimization methods. Part 1: Clustering methods,”*Mathematical Programming* 39 (1987) 27–56.

[59]

A.H.G. Rinnooy Kan and G.T. Timmer, “Stochastic global optimization methods. Part 2: Multi level methods,”*Mathematical Programming* 39 (1987) 57–78.

[60]

R.Y. Rubinstein,*Monte Carlo Optimization, Simulation and Sensitivity of Queuing Networks* (Wiley, New York, 1986).

[61]

K. Schittkowski,*More Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems No. 282* (Springer, Heidelberg, 1987).

[62]

S. Sengupta, “Global nonlinear constrained optimization,” Ph.D. Thesis, Department of Pure and Applied Mathematics, Washington State University (Pullman, WA, 1981).

[63]

C.H. Slump and B.J. Hoenders, “The determination of the location of the global maximum of a function in the presence of several local extrema,”*IEEE Transactions on Information Theory* IT-31 (1985) 490–497.

[64]

D.R. Stoutemyer, “Analytical optimization using computer algebraic manipulation,”*ACM Transactions on Mathematical Software* 1 (1975) 147–164.

[65]

D.R. Stoutemyer, “Automatic categorization of optimization problems: an application of computer symbolic mathematics,”*Operations Research* 26 (1978) 773–788.

[66]

P.T. Thach and H. Tuy, “Global optimization under Lipschitzian constraints,”*Japan Journal of Applied Mathematics* 4 (1987) 205–217.

[67]

J. Tomlin, “A suggested extension of special ordered sets to non-separable non-convex programming problems,” in P. Hansen, ed.,*Studies on Graphs and Discrete Programming, Annals of Discrete Mathematics* 11 (1981) 359–370.

[68]

A. Törn and A. Zilinkas,*Global Optimization. Lecture Notes in Computer Science No. 350* (Springer, New York, 1989).

[69]

G.W. Walster, E.R. Hansen and S. Sengupta, “Test results for a global optimization algorithm,” in: P.T. Boggs, R. Byrd and R. Schnabel, eds.,*Numerical Optimization 84* (SIAM, Philadelphia, PA, 1985) pp. 272–287.

[70]

D. Wilde, “Monotonicity and dominance in optimal hydraulic cylinder design,”*ASME Journal of Engineering for Industry* 97 (1975) 1390–1394.

[71]

R.S. Womersley, “Censored discrete linear ℓ_{1} approximation,”*SIAM Journal on Scientific and Statistical Computing* 7 (1986) 105–122.

[72]

P.B. Zwart, “Computational aspects on the use of cutting-planes in global optimization,”*Proceedings of the 1971 annual conference of the ACM* (1971) 457–465.