‘Smooth’ methods have been developed and used because under the assumption of smoothness it is possible to use the methods of differential calculus. For example, there are a great number of methods for solving convex optimization problems in which both the minimized objective and the set of feasible points can be expressed with the aid of differentiable convex functions. In some cases, however, the problems connected with the calculation of gradients have led to the development of algorithms which do not use derivatives. (Nevertheless, differentiability is still necessary to prove optimality, convergence assertions, etc.) The most successful optimization method — the well-known simplex method of linear programming — does not use derivatives. On the other hand, there are methods which make partial use of gradients, linearization etc., but which do not depend on differentiability assertions to prove their convergence.
- Feasible Point
- Differential Calculus
- Solve Optimization Problem
- Polyhedral Cone
- Independent Point
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Lommatzsch, K., Van Thoai, N. (1985). On Methods for Solving Optimization Problems without Using Derivatives. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_21
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