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Optimal Conditioning of Matrices
SIAM Journal on Numerical Analysis, 1973The optimal condition number c of a matrix S is the minimum, over all diagonal matrices D, of $\| {DS} \|\| {(DS)^{ - 1} } \|$. It arises in many applications of scaling in linear systems, and has been computed in the maximum norm by Bauer. In the $\ell _2 $-norm, we establish the inequalities $b \leqq c \leqq 2b$ and disprove—by an example of order ...
McCarthy, Charles, Strang, Gilbert
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Sufficient Optimality Conditions
Optimal Control, 2021L. T. Ashchepkov +3 more
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Regularity Conditions in Vector Optimization
Journal of Optimization Theory and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BIGI, GIANCARLO, PAPPALARDO, MASSIMO
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Global Optimality Conditions for Nonconvex Optimization
Journal of Global Optimization, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Optimality Conditions in Quasidifferentiable Optimization
SIAM Journal on Control and Optimization, 1984The paper is concerned with a class of quasidifferentiable functions in the sense of \textit{V. F. Demyanov} and \textit{A. M. Rubinov} [Dokl. Akad. Nauk SSSR 250, 21-25 (Russian) (1980; Zbl 0456.49016)]. Such functions are directionally differentiable and their directional derivatives are representable as a difference of two sublinear functions.
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Optimality conditions for global optimization (I)
Acta Mathematicae Applicatae Sinica, 1985With the help of the theory of measure and integration several global optimality conditions, which are sufficient and necessary, are given for minimizing a continuous function over a topological space.
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Necessary Optimality Conditions in Multiobjective Dynamic Optimization
SIAM Journal on Control and Optimization, 2004Let \(F: [a,b] \times \mathbb{R}^n \multimap \mathbb{R}^n\) be a closed-valued multimap, measurable in the first argument and sub-Lipschitzean in the second one; \(S \subset \mathbb{R}^n \times \mathbb{R}^n\) a nonempty closed set and \(f: \mathbb{R}^n \times \mathbb{R}^n \rightarrow \mathbb{R}^m\) a map. Extending the result of \textit{A.
Bellaassali, Saïd, Jourani, Abderrahim
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Optimality Conditions for Rank-Constrained Matrix Optimization
Journal of the Operations Research Society of China, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin-Rong Li, Wen Song, Nai-Hua Xiu
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Second-Order Optimality Conditions in Set Optimization
Journal of Optimization Theory and Applications, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jahn, J., Khan, A. A., Zeilinger, P.
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Network optimality conditions Network optimality conditions
2023Osmolovskii, Nikolai P +2 more
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