Directional derivatives of optimal solutions in smooth nonlinear programming

Solutions of Smooth Nonlinear Partial Differential Equations

and Applied Analysis 3 definition, it may happen that such a solution does not belong to any of the customary spaces of generalized functions. For example, given a function u : C \ {z0} −→ C 1.3 which is analytic everywhere except at the single point z0 ∈ C, and with an essential singularity at z0, Picard’s Theorem states that u attains every complex value, with possibly one exception, in every...

Optimal Control and Nonlinear Programming

In this thesis, we have two distinct but related subjects: optimal control and nonlinear programming. In the first part of this thesis, we prove that the value function, propagated from initial or terminal costs, and constraints, in the form of a differential equation, satisfy a subgradient form of the Hamilton-Jacobi equation in which the Hamiltonian is measurable with respect to time. In the ...

Multiple Optimal Solutions in Quadratic Programming Models

The problem of determining whether quadratic programming models possess either unique or multiple optimal solutions is important for empirical analyses which use a mathematical programming framework. Policy recommendations which disregard multiple optimal solutions (when they exist) are potentially incorrect and less than efficient. This paper proposes a strategy and the associated algorithm fo...

Research Article Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming

We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem...

Nonlinear Programming 2nd Edition Solutions Manual