By Tien van Do, Hoai An Le Thi, Ngoc Thanh Nguyen (eds.)
The complaints includes 30 papers that have been chosen and invited from the submissions to the 2nd foreign convention on computing device technology, utilized arithmetic and Applications (ICCSAMA 2014) hung on 8-9 may perhaps, 2014 in Budapest, Hungary. The convention is geared up into 7 periods: complex Optimization equipment and Their purposes, Queueing types and function assessment, software program improvement and trying out, Computational tools for cellular and instant Networks, Computational tools for wisdom Engineering, common sense established equipment for determination Making and knowledge Mining and Nonlinear structures and purposes, respectively. All chapters within the booklet speak about theoretical and sensible concerns attached with computational tools and optimization tools for wisdom engineering. The editors wish that this quantity should be worthwhile for graduate and Ph.D. scholars and researchers in machine technological know-how and utilized arithmetic. it's the wish of the editors that readers of this quantity can locate many inspiring rules and use them to their examine. Many such demanding situations are instructed by way of specific techniques and versions provided in person chapters of this book.
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Extra info for Advanced Computational Methods for Knowledge Engineering: Proceedings of the 2nd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 2014)
However, a new nonlinear nonconvex equality constraint W = xxT is introduced in the later one which destroyed the convexity of (3). The following lemma gives us an equivalent formulation to this equality. N Lemma 1 (see ). Let W ∈ S+ deﬁned as W := xxT . The constraint T W = xx is equivalent to W x 0 (4) xT 1 N T race(W − xxT ) = T race(W ) − x2i ≤ 0 i=1 (5) DCA for BMI/QMI Feasibility Problems 41 This lemma represents the nonlinear equality W = xxT as a LMI (4) with a reverse convex constraint (5).
43] had pointed out that BMIFP belongs to the class of DC (diﬀerence of convex functions) optimization problems. Some DC reformulation of BMIFP and algorithms based on branch and bound approach have been investigated in that paper. Later, a Lagrangian dual global optimization algorithm is proposed by the same author in . A sequence of concave minimization problems and DC programs were employed by Liu and Papavassilopoulos  on the same problem of Tuan. Mesbahi and Papavassilopoulos  have studied the theoretical aspects of the BMI and established equivalent formulations of cone programming.
A. N. Huynh, and T. Pham Dinh standard DC programs. That is the reason why we will not distinguish between standard and extended DCAs and all these algorithms will be called DCA for short. We hope this work will provide a deep understanding of these theoretical and algorithmic tools for researchers and practitioners to eﬃciently model and solve their real-word nonconvex programs, especially in the large-scale setting. References 1. html 2. : Convex analysis approach to DC programming: Theory, Algorithms and Applications.
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