Results 231 to 240 of about 11,355 (263)
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On the Hessian of Lagrangian and Second Order Optimality Conditions
SIAM Journal on Control and Optimization, 1986For 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, 2004In 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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On second-order optimality conditions in optimal control
2016 International Conference on Information and Digital Technologies (IDT), 2016We 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 conditions for bilevel set optimization problems
Journal of Global Optimization, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephan Dempe, Nazih Abderrazzak Gadhi
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Second-Order Optimality Condition for ΔH-Matrices
BIT Numerical Mathematics, 2003A \(\Delta H\) 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 note on second-order optimality conditions
Nonlinear Analysis: Theory, Methods & Applications, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Second-Order Optimality Conditions for Interval-Valued Optimization Problem
Asia-Pacific Journal of Operational ResearchIn this paper, we discuss the second-order KKT-type optimality conditions for interval-valued optimization problem. To derive second-order necessary and sufficient conditions, we use two different methodologies: square slack variable method and the theory of geometric cone optimality conditions for interval-valued objective functions.
Sachin Rastogi, Akhlad Iqbal
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On second-order conditions in vector optimization [PDF]
, 2002 Starting from second-order conditions for C 1,1 scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C 1,1 vector optimization problems can be derived.
Ginchev Ivan +2 more
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A New Approach to Second Order Optimality Conditions in Vector Optimization
1997The 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 +2 more
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Second order optimality conditions with applications
2007The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a point. An implementation of this algorithm, called cotcot, is available online and based on recent devel- opments in geometric optimal control.
Bonnard, Bernard +2 more
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