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Second-Order Optimality Conditions in Minimax Optimization Problems
Journal of Optimization Theory and Applications, 2012A finite-dimensional minimax problem \(\min_{x} \sup_{y\in Y} f(x,y)\) s.t. \(g(x)\in D\), \(h(x)=0\) with \(x\in \mathbb R^n\), \(Y\subset \mathbb R^m\) compact, \(D\subset \mathbb R^m\) closed with nonempty interior, \(f(\cdot,y),y\in Y\); \(g\); \(h\) \(C(1,1)\) functions is reformulated and dealt with cone constraint as infinite programming problem
Dhara, Anulekha, Mehra, Aparna
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Second Order Optimality Conditions
2004In 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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Mollified Derivatives and Second-order Optimality Conditions
SSRN Electronic Journal, 2003The authors provide new generalized differentiability notions of first and of second-order for integrable (not necessary continuous) functions \(f:\mathbb{R}^m \to\mathbb{R}\) by means of families of so-called mollifiers and associated sequences of mollified functions.
LA TORRE D. +2 more
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Second Order Necessary Conditions in Optimization
SIAM Journal on Control and Optimization, 1984The 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 Optimality Conditions for Nonsmooth Multiobjective Optimization Problems
SSRN Electronic Journal, 2002In 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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On Second Order Necessary Conditions of Optimality
SIAM Journal on Control, 1969Second order necessary conditions of optimality with straightforward application to nonlinear programming of optimal control ...
Messerli, E. J., Polak, E.
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Second-Order Enhanced Optimality Conditions and Constraint Qualifications
Journal of Optimization Theory and Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuang Bai, Yixia Song, Jin Zhang
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Alternative Second-Order Conditions in Constrained Optimization
Journal of Optimization Theory and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiss, H., Ben-Asher, J. Z.
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Second-Order Optimality Conditions for Constrained Domain Optimization
Journal of Optimization Theory and Applications, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
SIAM Journal on Optimization, 1999Summary: We discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second ...
Bonnans, J. Frédéric +2 more
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