caa a22 4500 469067756 CHVBK 20180323132913.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF00121303 doi (NATIONALLICENCE)springer-10.1007/BF00121303 Unconstrained and constrained global optimization of polynomial functions in one variable [Elektronische Daten] [V. Visweswaran, C. Floudas] In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated. Kluwer Academic Publishers, 1992 Global optimization nationallicence polynomial functions nationallicence unconstrained and constrained optimization nationallicence the GOP algorithm nationallicence Visweswaran V. Chemical Engineering Department, Princeton University, 08544-5263, Princeton, N.J., U.S.A. aut Floudas C. Chemical Engineering Department, Princeton University, 08544-5263, Princeton, N.J., U.S.A. aut Journal of Global Optimization Kluwer Academic Publishers 2/1(1992-03-01), 73-99 0925-5001 2:1<73 1992 2 10898 https://doi.org/10.1007/BF00121303 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00121303 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Visweswaran V. Chemical Engineering Department, Princeton University, 08544-5263, Princeton, N.J., U.S.A aut NATIONALLICENCE 700 1- Floudas C. Chemical Engineering Department, Princeton University, 08544-5263, Princeton, N.J., U.S.A aut NATIONALLICENCE 773 0- Journal of Global Optimization Kluwer Academic Publishers 2/1(1992-03-01), 73-99 0925-5001 2:1<73 1992 2 10898 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer