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Journal of Optimization Theory and Applications, 2000
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Salmon, Genevieve +2 more
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Salmon, Genevieve +2 more
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Convergence analysis of an extended auxiliary problem principle with various stopping criteria
Optimization Methods and Software, 2011We investigate the Extended Proximal Auxiliary Problem Principle (EPAPP) [A. Kaplan and R. Tichatschke, Extended Auxiliary Problem Principle using Bregman distances, Optimization 53 (2004), pp. 603-623, A. Kaplan and R. Tichatschke, Bregman functions and auxiliary problem principle, Optim. Methods Softw. 23, 1 (2008), pp.
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Journal of Optimization Theory and Applications, 2010
Let \(B\) be a Banach space with dual \(B^*\). Let \(\|\cdot\|\) be the norm of \(B\) and \(\langle\cdot,\cdot\rangle\) the duality pairing between \(B\) and \(B^*\). Let \(C\) be a nomempty closed convex subset of \(B\). Let \(F,H: C\times C\to\mathbb{R}\) and \(\psi,\phi: B\times B\to\mathbb{R}\) be four bifunctions.
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Let \(B\) be a Banach space with dual \(B^*\). Let \(\|\cdot\|\) be the norm of \(B\) and \(\langle\cdot,\cdot\rangle\) the duality pairing between \(B\) and \(B^*\). Let \(C\) be a nomempty closed convex subset of \(B\). Let \(F,H: C\times C\to\mathbb{R}\) and \(\psi,\phi: B\times B\to\mathbb{R}\) be four bifunctions.
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Auxiliary Principle Technique for Hierarchical Equilibrium Problems
Journal of Optimization Theory and Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pham Ngoc Anh, Qamrul Hasan Ansari
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DC auxiliary principle methods for solving lexicographic equilibrium problems
Journal of Global Optimization, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pham Ngoc Anh +2 more
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Auxiliary Problem Principle and Proximal Point Methods
Journal of Global Optimization, 2000In 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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Distributed Multi-Period DCOPF via an Auxiliary Principle Problem Algorithm
2021 IEEE Texas Power and Energy Conference (TPEC), 2021Distributed 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, 2013Let 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 Technique for Equilibrium Problems
Journal of Optimization Theory and Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2020 55th International Universities Power Engineering Conference (UPEC), 2020
Voltage optimization is a key management issue in active distribution systems that can be tackled by acting on the reactive powers provided by distributed generators. Due to the large number of nodes, distributed algorithms are preferable to solve the optimization problem with limited measurements and information exchange.
Anna Rita Di FAZIO +3 more
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Voltage optimization is a key management issue in active distribution systems that can be tackled by acting on the reactive powers provided by distributed generators. Due to the large number of nodes, distributed algorithms are preferable to solve the optimization problem with limited measurements and information exchange.
Anna Rita Di FAZIO +3 more
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