Second-Order Sufficient Optimality Conditions in the Calculus of Variations
Journal of Optimization Theory and ApplicationsSome classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear second-order initial value problem and check that the solution is positive over the problem domain.
William W. Hager
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Necessary and Sufficient Second-Order Optimality Conditions on Hadamard Manifolds
Mathematics, 2020 This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of ...
Gabriel Ruiz-Garzón +3 more
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First and second order necessary optimality conditions for discrete optimal control problems [PDF]
Yugoslav Journal of Operations Research, 2006 Discrete optimal control problems with varying endpoints are considered. First and second order necessary optimality conditions are obtained without normality assumptions.
Marinković Boban
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Second-order conditions for non-uniformly convex integrands: quadratic growth in $L^1$ [PDF]
Journal of Nonsmooth Analysis and Optimization, 2022 We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures.
Daniel Wachsmuth, Gerd Wachsmuth
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Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations
Advances in Difference Equations, 2007 We discuss the existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive differential equations in infinite dimensional spaces.
Y. Peng, X. Xiang, W. Wei
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Second-order optimality conditions for bilevel programs [PDF]
, 2023 Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions, which can not be ...
Zhang, Liwei, Liu, Xiang, Xu, Mengwei
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An optimal control problem for the systems with integral boundary conditions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In this paper, we consider an optimal control problem with a «pure», integral boundary condition. The Green’s function is constructed. Using contracting Banach mappings, a sufficient condition for the existence and uniqueness of a solution to ...
M.J. Mardanov, Y.A. Sharifov
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On Necessary Optimality Conditions for Discrete Control Systems
Известия Иркутского государственного университета: Серия "Математика", 2020 In this article, under weakened assumptions, we study high-order necessary optimality conditions for discrete optimal control problems with the free right end of the trajectory.
M. J. Mardanov, T. K. Melikov
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Mathematics, 2022 This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality of second-order for a set-valued fractional minimax problem.
Koushik Das +2 more
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Necessary and sufficient condition on global optimality without convexity and second order differentiability [PDF]
, 2012 The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function
Burai, Pál
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