Journal ArticleDOI
Sensitivity analysis for nonlinear programming using penalty methods
TLDR
A theoretical basis is established for utilizing a penalty-function method to estimate sensitivity information of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions.Abstract:
In this paper we establish a theoretical basis for utilizing a penalty-function method to estimate sensitivity information (i.e., the partial derivatives) of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions. The local solution is assumed to satisfy the second order sufficient conditions for a strict minimum. Although theoretically valid for higher order derivatives, the analysis concentrates on the estimation of the first order (first partial derivative) sensitivity information, which can be explicitly expressed in terms of the problem functions. For greater clarity, the results are given in terms of the mixed logarithmic-barrier quadratic-loss function. However, the approach is clearly applicable toany algorithm that generates a once differentiable "solution trajectory".read more
Citations
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Journal ArticleDOI
The explicit linear quadratic regulator for constrained systems
TL;DR: A technique to compute the explicit state-feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints is presented, and it is shown that this closed form solution is piecewise linear and continuous.
Book
Predictive Control for Linear and Hybrid Systems
TL;DR: Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
Journal ArticleDOI
Strongly Regular Generalized Equations
TL;DR: A regularity condition is introduced for generalized equations and it is shown to be in a certain sense the weakest possible condition under which the stated properties will hold.
Journal ArticleDOI
An explicit solution to the multi-level programming problem
Jonathan F. Bard,James E. Falk +1 more
TL;DR: The bi-level linear case is addressed in detail and the reformulated optimization problem is linear save for a complementarity constraint of the form 〈u, g〉 = 0.
Journal ArticleDOI
Sensitivity Analysis of Discrete Structural Systems
TL;DR: In this paper, a survey of sensitivity derivatives for discrete structural systems is presented, primarily focusing on publications developed in nonstructural fields such as electronics, control, and physical chemistry which are directly applicable to structural problems.
References
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Book
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.