A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals
Authors:
- Dimitri P. BertsekasDBDimitri P. Bertsekas
- Sanjoy K. MitterSMSanjoy K. Mitter
- 1 November 1973
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control
- Vol. 11 (4) , 637-652
Abstract
In this paper we consider the numerical solution of convex optimization problems with nondifferentiable cost functionals. We propose a new algorithm, the $\varepsilon $-subradient method, a large step, double iterative algorithm which converges rapidly under very general assumptions. We discuss the application of the algorithm in some problems of nonlinear programming and optimal control and we show that the $\varepsilon $-subgradient method contains as a special case a minimax algorithm due to Pshenichnyi [5].Keywords
This publication has 18 references indexed in Scilit:
- Optimality Criteria in Nonlinear Programming Without DifferentiabilityOperations Research, 1971
- Convex Analysis1970
- Conjugate convex functions in optimal control and the calculus of variationsJournal of Mathematical Analysis and Applications, 1970
- Control problems with kinksIEEE Transactions on Automatic Control, 1970
- Conjugate convex functions, duality, and optimal control problems I: Systems governed by ordinary differential equationsInformation Sciences, 1970
- A general theory of extremalsJournal of Computer and System Sciences, 1969
- Minimization of Functionals in Normed SpacesSIAM Journal on Control, 1968
- The Theory of Max-Min, with ApplicationsSIAM Journal on Applied Mathematics, 1966
- Characterization of the subdifferentials of convex functionsPacific Journal of Mathematics, 1966
- On the subdifferentiability of convex functionsProceedings of the American Mathematical Society, 1965