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...................................................................... The increasing importance of mathematical programming for the solution of complex nonlinear systems arising in practical situations requires the development of qualified optimization software. In recent years, a lot of effort has been made to implement efficient and reliable optimization programs and we can observe a wide distribution of these programs both for research and industrial applications. In spite of their practical importance only a few attempts have been made in the past to come to comparative conclusions and to give a designer the possibility to decide which optimization program could solve his individual problems in the most desirable way. Box [BO 1966J, Huang, Levy [HL 1970J, Himmelblau [HI 1971J, Dumi tru [DU 1974], and More, Garbow, Hillstrom [MG 1978] for example compared algorithms for unres~ricied u~~illii~Gtiv~ y~~~le~~, B~~n [BD 1970], McKeown [MK 1975], and Ramsin, Wedin [RW 1977l studied codes for nonlinear least squares problems. Codes for the linear case are compared by Bartels [BA 1975.J and Schittkowski, Stoer [SS 1979J. Extensive tests for geometric programming algorithms are found in Dembo [DE 1976bJ, Rijckaert [RI 1977], and Rijckaert, Martens [RM 1978J.
List of contents
I: Introduction.- II: Optimization methods.- 1. Line-search algorithms.- 2. Quadratic programming.- 3. Unconstrained optimization.- 4. Penalty methods.- 5. Multiplier methods.- 6. Quadratic approximation methods.- 7. Generalized reduced gradient methods.- 8. The method of Robinson.- III: Optimization programs.- 1. Program organization.- 2. Description of the programs.- IV: The construction of test problems.- 1. Fundamentals of the test problem generator.- 2. General test problems.- 3. Linearly constrained test problems.- 4. Degenerate test problems.- 5. Ill-conditioned test problems.- 6. Indefinite test problems.- 7. Convex test problems.- V: Performance evaluation.- 1. Notations.- 2. Efficiency, reliability, and global convergence.- 3. Performance for solving degenerate, ill-conditioned, and indefinite problems.- 4. Sensitivity to slight variations of the problem.- 5. Sensitivity to the position of the starting point.- 6. Ease of use.- 7. How to get a final score.- VI: Conclusions, recommendations, remarks.- 1. Pinal conclusions.- 2. Recommendations for the design of optimization programs.- 3. Some technical details.- Appendix A : Numerical data for constructing test problems.- Appendix B : Sensitivity analysis for the test problems.- Appendix C : Further results.- Appendix D : Evaluation of significance factors.- References.
