Results 261 to 270 of about 20,565,365 (293)

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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On the Classical Necessary Second-Order Optimality Conditions

Journal of Optimization Theory and Applications, 2004
In this paper a nonconvex optimization problem in \({\mathbb R}^n\) with equality and inequality constraints is considered. Assuming that the Mangasarian-Fromovitz constraint qualifications hold at a local optimal solution, the aim is to provide sufficient conditions that imply the necessary second-order conditions CN2, with the same Lagrange ...
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Second-order optimality conditions for minimizing a maxfunction

Science in China Series A: Mathematics, 2000
The authors consider the problem of minimizing the function \(h(x):=\max\{f(x,\tau)\mid \tau \in T\}\), where \(x\in R^{p}\), \(T\) is a compact metric space and the function \(f(\cdot ,\tau)\) is \(C^{2}\). Second-order necessary optimality conditions are obtained by using second-order directional derivatives of Chaney and Ben-Tal/Zowe of \(h\). These
Huang, Liren, Ng, K. F.
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Second-Order Optimality Conditions for Nonsmooth Multiobjective Optimization Problems

2004
In this paper second-order necessary optimality conditions for nonsmooth vector optimization problems are given by smooth approximations. We extend to the vector case the approach introduced by Ermoliev, Norkin and Wets to define generalized derivatives for discontinuous functions as limit of the classical derivatives of regular functions.
G. P. Crespi, D. La Torre, M. Rocca
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Second order optimality conditions in nonsmooth unconstrained optimization

1998
Summary: Second order necessary and sufficient conditions are given for a nonsmooth function \(f\) defined in a Banach space to attain a minimum at a point in the interior of its domain. At the beginning sufficient conditions in terms of Riemann type derivatives are introduced.
IVANOV, IVAN GINCHEV, GUERRAGGIO, ANGELO
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Second order optimality conditions in multiobjective programming

Optimization, 1998
In this paper we will establish some necessary and or sufficient optimality conditions for a vector maximization problem. These conditions are firstly stated without the use of any constraint qualifications. then the given approach allow us to introduce two different kinds of regularity conditions.
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On second-order optimality conditions in optimal control

2016 International Conference on Information and Digital Technologies (IDT), 2016
We observe some results obtained by the author on necessary and sufficient second-order conditions for the strong, bounded strong, Pontryagin's and weak local minimum in optimal control problems with control system, given by ordinary differential equations, considered on a fixed time interval, subject to control constraints and finite number of end ...
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Second-Order Optimality Condition for ΔH-Matrices

BIT Numerical Mathematics, 2003
A \(\Delta H\) matrix \(A\) is a square matrix that can be written as \(A=D+DH-HD\), for certain Hermitian \(H\) and diagonal \(D\). \textit{A. Ruhe} [BIT 27, 585--598 (1987; Zbl 0636.15017)] gave a necessary and sufficient condition to solve the problem of finding a normal matrix \(N\) realizing the Frobenius distance from \(A\) to the variety of ...
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A New Approach to Second Order Optimality Conditions in Vector Optimization

1997
The aim of this paper is to establish some second order necessary and sufficient optimality conditions for a multiobjective problem where optimality is studied with respect to arbitrary closed convex cones. The proposed approach is an extension to the one recently given by the same authors.
CAMBINI, ALBERTO, MARTEIN, LAURA, CAMBINI, RICCARDO   +2 more
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A note on second-order optimality conditions

Nonlinear Analysis: Theory, Methods & Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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