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Extended auxiliary problem principle using Bregman distances

Optimization, 2004
An extension of the Auxiliary Problem Principle (cf., G. Cohen (1980). Auxiliary problem principle and decomposition of optimization problems. JOTA, 32, 277–305; G. Cohen (1988). Auxiliary problem principle extended to variational inequalities. JOTA, 59, 325–333.) for solving variational inequalities with maximal monotone operators is studied.
A. Kaplan, R. Tichatschke
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Clines: an Auxiliary Taxonomic Principle

Nature, 1938
MODERN taxonomy, after a phase of 'splitting', adopted the integrating principle of geographical replacement, thus uniting numerous forms previously styled species as geographical races or subspecies of a polytypic species or Formenkreis1. It seems desirable, however, to go still further in the direction of synthesis.
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Auxiliary Principle Technique for Hierarchical Equilibrium Problems

Journal of Optimization Theory and Applications, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pham Ngoc Anh, Qamrul Hasan Ansari
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Chiral Auxiliaries — Principles and Recent Applications

ChemInform, 2006
AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.
Frank Glorius, Yvonne Gnas
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Auxiliary Problem Principle and Proximal Point Methods

Journal of Global Optimization, 2000
In the present paper the auxiliary problem principle (APP) of \textit{G. Cohen} [J. Optimization Theory Appl. 59, No. 2, 325-333 (1988; Zbl 0628.90066)] is studied for variational inequalities of the type of finding \(x^* \in K: \langle {\mathcal F}(x^*)+ {\mathcal Q} (x^*), x-x^*\rangle \geq 0\) \(\forall x \in K\), where K is a convex closed subset ...
Kaplan, A., Tichatschke, R.
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DC auxiliary principle methods for solving lexicographic equilibrium problems

Journal of Global Optimization, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pham Ngoc Anh   +2 more
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Distributed Multi-Period DCOPF via an Auxiliary Principle Problem Algorithm

2021 IEEE Texas Power and Energy Conference (TPEC), 2021
Distributed algorithms provide attractive features for solving Optimal Power Flow (OPF) problems in interconnected power systems compared to traditional centralized algorithms. Distributed algorithms help to maintain the control autonomy and data privacy of subsystems, which is particularly relevant in competitive markets and practical control system ...
Mohannad Alkhraijah   +3 more
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Auxiliary Principle Technique for Solving Split Feasibility Problems

Applied Mathematics & Information Sciences, 2013
Let K and C be nonempty, closed and convex sets in R n and R m respectively and A be an m £ n real matrix. The split feasibility problem is to find u 2 K with Au 2 C: Many problems arising in the image reconstruction can be formulated in this form.
Muhammad Noor, Khalida Noor
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Auxiliary Principle and Iterative Algorithms for Lions-Stampacchia Variational Inequalities

Journal of Optimization Theory and Applications, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xia, F. Q., Huang, N. J.
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On Auxiliary Principle for Equilibrium Problems

2003
The auxiliary problem principle introduced by Cohen is extended to a general equilibrium problem. In particular, applications to variational inequalities and to convex optimization problems are analysed.
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