Results 221 to 230 of about 100,213 (248)

Second Order Optimality Conditions

2004
In this chapter we obtain second order necessary optimality conditions for control problems. As we know, geometrically the study of optimality reduces to the study of boundary of attainable sets (see Sect. 10.2). Consider a control system $$\dot q = {f_u}(q),q \in M,u \in U = \operatorname{int} U \subset {R^m},$$ (20.1) where the state space ...
Andrei A. Agrachev, Yuri L. Sachkov
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Second Order Conditions for Pseudo-Convex Functions

SIAM Journal on Applied Mathematics, 1974
A necessary condition and a sufficient condition for the pseudo-convexity of a function are given. These conditions involve the Hessian matrix and the gradient vector of the function and present the advantage of reducing the recognition of pseudo-convexity to the checking of the positive semidefiniteness of a matrix. In the case of a quadratic function
Mereau, Pierre, Paquet, Jean-Guy
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On the Second-Order Sufficiency Conditions

Journal of Information and Optimization Sciences, 1983
In this remark the differential geometric interpretation of a second order optimality condition is given. On this basis the sufficient condition can be checked by calculating the greatest eigenvalue of a matrix, given explicitly by using the gradient vector and the Hessian matrix.
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Mollified Derivatives and Second-order Optimality Conditions

SSRN Electronic Journal, 2003
The authors provide new generalized differentiability notions of first and of second-order for integrable (not necessary continuous) functions \(f:\mathbb{R}^m \to\mathbb{R}\) by means of families of so-called mollifiers and associated sequences of mollified functions.
LA TORRE D., ROCCA, MATTEO, CRESPI, GIOVANNI PAOLO   +2 more
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Geometric local controllability: second-order conditions

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2003
The notion of a control-affine system is abstracted to its geometric essence: an affine subbundle. The notions of control systems and controllability are presented, and general second-order conditions for local controllability are given. The conditions are notable in that their hypotheses involve only the affine subbundle, and objects directly related ...
Ronald M. Hirschorn, Andrew D. Lewis
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Second-order conditioning of Pavlovian conditioned inhibition

Learning and Motivation, 1976
Abstract Two experiments are reported which investigated the conditioning of inhibition to a neutral stimulus as a result of its repeated pairing with a previouslyconditioned inhibitor. Both experiments employed a conditioned suppression technique with rat subjects. Experiment 1 detected the second-order inhibition through the retarded acquisition of
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Second-Order Conditions for Optimization Problems with Constraints

SIAM Journal on Control and Optimization, 1998
The author obtains necessary or sufficient second-order optimality conditions for constrained optimization problems. The main novelty is to work in a projective space (space of directions), which allows to improve the known results.
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Second-order necessary conditions in semismooth optimization

Mathematical Programming, 1988
This is the second in a series of four closely related papers by the same author. These works introduce a new concept of second-order directional derivative for nonsmooth functions, and demonstrate its applicability to the study of necessary and sufficient conditions for optimality in finite-dimensional mathematical programming.
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Aversive second-order conditioning in the pigeon: Elimination of conditioning to CS1 and effects on established second-order conditioning.

Canadian Journal of Psychology / Revue canadienne de psychologie, 1982
M, Hittesdorf, R W, Richards
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On the Hessian of Lagrangian and Second Order Optimality Conditions

SIAM Journal on Control and Optimization, 1986
For a constrained minimization problem, the restriction of the Hessian of the Lagrangian to a tangent space of the feasible set can be used to characterize a Karush-Kuhn-Tucker point of the problem as a local minimum, maximum or saddle point. It is shown in this paper that the restriction of the Hessian to a normal space with respect to the indefinite ...
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