Results 241 to 250 of about 14,708,080 (276)

Second-Order Conditions

2018
Second-order conditions for both parameter optimization problems and optimal control problems are analysed. A new conjugate point test procedure is discussed and illustrated. For an optimal control problem we will examine the second variation of the cost. The first variation subject to constraints provides first-order NC for a minimum of J.
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Second Order Necessary Conditions in Optimization

SIAM Journal on Control and Optimization, 1984
The author considers an optimization problem which contains restrictions in the form of finitely many equalities and of inclusions involving an arbitrary convex body in a normed vector space, i.e. Q is a convex subset of a real vector space, H is a normed vector space, C is a convex body in H, \((\phi_ 0,\phi_ 1,\phi_ 2):Q\to {\mathbb{R}}\times ...
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Second Order Conditions for Constrained Minima

SIAM Journal on Applied Mathematics, 1967
This paper establishes two sets of "second order" conditions-one which is necessary, the other which is sufficient-in order that a vector x* be a local minimum to the constrained optimization problem: minimize f(x) subject to the constraints \( g_{i}(x)\geqq 0,i=1,\cdots ,m,\; \rm{and} \; h_{i}(x)=0,j=1,\cdots,p, \) where the problem functions are ...
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Second order optimality conditions

Journal of Discrete Mathematical Sciences and Cryptography, 2000
Abstract The aim of the paper is to establish some new second order optimality conditions by means of suitable second order tangent sets.
MARTEIN, LAURA, A. CAMBINI
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Second order conditions

1995
For a thin dielectric layer, second order transition conditions were developed by Weinstein (1969) and used (Leppington, 1983) to determine the field diffracted by an abrupt change in layer thickness. Since then there have been numerous applications of second (and higher) order boundary conditions in electromagnetics, but some of the solutions are ...
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Second-Order Conditions

1990
Abstract The previous chapter developed sufficient conditions for optimality, using properties like concavity and quasi-concavity. These were defined globally, that is, over the full domain of definition of the functions. For example, a function is called concave if the tangent at any point lies on or above the graph of the function ...
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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 Sufficient Conditions in Nonsmooth Optimization

Mathematics of Operations Research, 1988
Second-order conditions are given which are sufficient to guarantee that a given point be a local solution to certain types of finite-dimensional nonsmooth nonlinear programming problems. Both unconstrained and constrained problems are considered.
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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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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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