Kegl, M.; Oblak, M. M. Optimization of mechanical systems: On non-linear first-order approximation with an additive convex term. (English) Zbl 0878.65048 Commun. Numer. Methods Eng. 13, No. 1, 13-20 (1997). The authors develop an approximation technique for gradient based approximation methods of mathematical programming. The new method uses an additive convex term for each conventional approximating function. Numerical examples state that the approximation with a convex term can be employed efficiently on problems that tend to yield highly oscillating sequences of approximate solutions. Reviewer: F.Luban (Bucureşti) Cited in 6 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 70F99 Dynamics of a system of particles, including celestial mechanics Keywords:mechanical systems; numerical examples; gradient based approximation methods; additive convex term PDF BibTeX XML Cite \textit{M. Kegl} and \textit{M. M. Oblak}, Commun. Numer. Methods Eng. 13, No. 1, 13--20 (1997; Zbl 0878.65048) Full Text: DOI References: [1] Oblak, Minimum weight design of trusses by an optimality criteria method, Z. Angew. Math. Mech. 69 pp T93– (1989) · Zbl 0677.73067 [2] Kegl, Optimal design of conventional in-line fuel injection equipment, Proc. Inst. Mech. Eng. - Part D: J. Autom. Eng. 209 pp 135– (1995) · doi:10.1243/PIME_PROC_1995_209_194_02 [3] Fleury, Structural optimization: A new dual method using mixed variables, Int. J. numer. methods eng. 23 pp 409– (1986) · Zbl 0585.73152 · doi:10.1002/nme.1620230307 [4] Svanberg, The method of moving asymptotes - A new dual method for structural optimization, Int. j. numer. methods eng. 24 pp 359– (1987) · Zbl 0602.73091 · doi:10.1002/nme.1620240207 [5] Kegl, Optimization of mechanical systems: On strategy of non-linear first-order approximation, Int. j. numer. methods eng. 33 pp 223– (1992) · Zbl 0757.73036 · doi:10.1002/nme.1620330202 [6] Oblak, An approach to optimal design of structures with non-linear response, Int. j. numer. methods eng. 36 pp 511– (1993) · Zbl 0770.73051 · doi:10.1002/nme.1620360309 [7] Kegl, Shape optimal design of elastic planar frames with non-linear response, Int. j. numer. methods eng. 38 pp 3227– (1995) · Zbl 0849.73044 · doi:10.1002/nme.1620381904 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.