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On second–order Taylor expansion of critical values

Stephan Bütikofer, Diethard Klatte, Bernd Kummer (2010)

Kybernetika

Studying a critical value function $ϕ$ in parametric nonlinear programming, we recall conditions guaranteeing that $ϕ$ is a $C^{1, 1}$ function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of $D ϕ$ . Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization....

On some properties of paramonotone operators.

Iusem, Alfredo N. (1998)

Journal of Convex Analysis

On some sufficient optimality conditions in multiobjective differentiable programming

Vasile C. Preda (1992)

Kybernetika

On sufficient conditions of optimality of second order

S. Rolewicz (1983)

Annales Polonici Mathematici

On superlinear multiplier update methods for partial augmented Lagrangian techniques.

Eugenio Mijangos (2002)

Qüestiió

The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting in case that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to carry out...

On the acceleration of adaptation processes by two-step principles

Klaus Fritzsch (1977)

Kybernetika

On the Ball Spanned by Balls.

N. Megiddo (1989)

Discrete & computational geometry

On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints.

Eugenio Mijangos Fernández, Narcís Nabona Francisco (1999)

Qüestiió

The minimization of a nonlinear function subject to linear and nonlinear equality constraints and simple bounds can be performed through minimizing a partial augmented Lagrangian function subject only to linear constraints and simple bounds by variable reduction techniques. The first-order procedure for estimating the multiplier of the nonlinear equality constraints through the Kuhn-Tucker conditions is analyzed and compared to that of Hestenes-Powell. There is a method which identifies those major...