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Smoothing Method for Minimax Problems
Computational Optimization and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Minimax estimation methods under ellipsoidal constraints
Automation and Remote Control, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mamaev, A. A., Semenikhin, K. V.
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Introduction to Minimax Methods
2011This chapter is an introduction to a broad class of methods that have been shown to be extremely useful in a variety of contexts.
Marino Badiale, Enrico Serra
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Numerical methods for linear minimax estimation
Discussiones Mathematicae Probability and Statistics, 2000Summary: We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior ...
Gaffke, Norbert, Heiligers, Berthold
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RAP-method (random perturbation method) for minimax G-filter
Random Operators and Stochastic Equations, 2020Abstract The spectral equations for the minimax estimates of the parameters of some systems are obtained.
Girko, Vyacheslav L. +2 more
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Smooth Optimization Methods for Minimax Problems
SIAM Journal on Control and Optimization, 1988The classical discrete minimax problem is considered. It is transformed into an equivalent problem by a monotone transformation of the initial functions. It was found that the classical Lagrangian of the equivalent problem has a number of important properties both in primal and dual spaces in convex as well as in nonconvex cases.
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Minimax Methods for Inequality Problems
2003We know from Chapter 2 that, if we intend to consider concrete problems in unilateral Mechanics involving both monotone and nonmonotone unilateral boundary (or interior) conditions, then we have in general to deal with a nonsmooth and nonconvex energy functional — expressed as the sum of a locally Lipschitz function \(\Phi :X \to \mathbb{R}\) and a ...
D. Goeleven +3 more
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An Iterative Method for the Minimax Problem
1995The authors propose a class of iteration methods for the minimax problem \({\displaystyle {\min_{x \in X} \max_{y \in Y}}} L(x,y)\), where \(L\) is a convex-concave function from \(X \times Y\) to \([- \infty, + \infty]\) and \(X\) and \(Y\) are closed nonempty convex sets in \(\mathbb{R}^n\) and \(\mathbb{R}^m\), respectively, \(X = \{z / c_i (x) \leq
Qi, Liqun, Sun, Wenyu
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Solving minimax problems by interval methods
BIT, 1990Interval arithmetic offers various tests (monotonicity test, convexity test, etc.) and methods (Newton's method, bisection, etc.) for solving global optimization problems with prescribed accuracy. The paper shows that these tests can be extended to solve global minimax problems. An algorithm as well as two numerical examples are included.
Shen, Zuhe +2 more
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Stochastic methods for solving minimax problems
Cybernetics, 1984In applying methods of operations research to economics, planning, control, optimization of complex technical systems, optimal design, and to other areas it frequently becomes necessary to solve minimax problems of the following form: \[ (1)\quad \min_{u\in U}\max_{x\in X}f(x,u),\quad U\subset E^ m,\quad X\subset E^ n.
Ermoliev, Y., Gaivoronski, A.A.
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