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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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On the Second-Order Sufficiency Conditions
Journal of Information and Optimization Sciences, 1983In 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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On second order conditions for quasiconvexity
Mathematical Programming, 1980The paper presents a sufficient condition for quasiconvexity in terms of Hessian, hereby extending an earlier result by Katzner in 1970, and (by a slight modification of the assumptions) a necessary and sufficient condition for quasiconvexity.
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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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Second-order aversive classical conditioning.
Canadian Journal of Psychology / Revue canadienne de psychologie, 1967D. Chris Anderson +2 more
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Conditioned reinforcement in second-order schedules.
Journal of the experimental analysis of behavior, 1967Pigeons responded under a schedule in which food was presented only after a fixed number of fixed-interval components were completed. Two such second-order schedules were studied: under one, 30 consecutive 2-min fixed-interval components were required; under the other, 15 consecutive 4-min fixed-interval components were required.
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