Abstract
In order for primal-dual methods to be applicable to a constrained minimization problem, it is necessary that restrictive convexity conditions are satisfied. In this paper, we consider a procedure by means of which a nonconvex problem is convexified and transformed into one which can be solved with the aid of primal-dual methods. Under this transformation, separability of the type necessary for application of decomposition algorithms is preserved. This feature extends the range of applicability of such algorithms to nonconvex problems. Relations with multiplier methods are explored with the aid of a local version of the notion of a conjugate convex function.
Original language | English (US) |
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Pages (from-to) | 169-197 |
Number of pages | 29 |
Journal | Journal of Optimization Theory and Applications |
Volume | 29 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1979 |
Externally published | Yes |
Keywords
- Primal-dual methods
- convexification procedures
- decomposition methods
- local convex conjugate functions
- multiplier methods
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics