Abstract
In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of a path of optimal solutions generated by nonlinear Lagrangian problems and show its convergence toward the optimal set of the original problem. We analyze the convergence of several classes of nonlinear Lagrangian problems in terms of their first and second order necessary optimality conditions.
Original language | English |
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Pages (from-to) | 1119-1144 |
Number of pages | 26 |
Journal | SIAM Journal on Optimization |
Volume | 11 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Mar 2001 |
Keywords
- Augmented Lagrangian
- Necessary optimality condition
- Nonlinear Lagrangian
- Optimal path
- Smooth approximate variational principle
- Zero duality gap
ASJC Scopus subject areas
- Theoretical Computer Science
- Software