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Duality in Constrained DC-Optimization via Toland’s Duality Approach

Laghdir, M., Benkenza, N. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 90C48, 49N15, 90C25In this paper we reconsider a nonconvex duality theory established by B. Lemaire and M. Volle (see [4]), related to a primal problem of minimizing the difference of two convex functions subject to a DC-constraint. The purpose of this note is to present a new method based on Toland-Singer duality principle. Applications to the case when the constraints are vector-valued are provided.

Duality theorems for a class of non-linear programming problems.

Shyam S. Chadha (1988)

Trabajos de Investigación Operativa

Duality of linear programming is used to establish an important duality theorem for a class of non-linear programming problems. Primal problem has quasimonotonic objective function and a convex polyhedron as its constraint set.

Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities

M. Hintermüller, R. H. W. Hoppe, C. Löbhard (2014)

ESAIM: Control, Optimisation and Calculus of Variations

A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical...

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