Advanced Computational Methods for Knowledge Engineering: by Tien van Do, Hoai An Le Thi, Ngoc Thanh Nguyen (eds.)

By Tien van Do, Hoai An Le Thi, Ngoc Thanh Nguyen (eds.)

The court cases contains 30 papers which were chosen and invited from the submissions to the 2nd foreign convention on desktop technological know-how, utilized arithmetic and Applications (ICCSAMA 2014) hung on 8-9 may possibly, 2014 in Budapest, Hungary. The convention is equipped into 7 classes: complex Optimization tools and Their purposes, Queueing versions and function assessment, software program improvement and trying out, Computational tools for cellular and instant Networks, Computational equipment for wisdom Engineering, common sense established equipment for choice Making and knowledge Mining and Nonlinear structures and functions, respectively. All chapters within the booklet speak about theoretical and functional matters attached with computational equipment and optimization equipment for wisdom engineering. The editors desire that this quantity could be important for graduate and Ph.D. scholars and researchers in machine technology and utilized arithmetic. it's the desire of the editors that readers of this quantity can locate many inspiring principles and use them to their examine. Many such demanding situations are recommended by means of specific ways and versions awarded in person chapters of this book.

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Additional info for Advanced Computational Methods for Knowledge Engineering: Proceedings of the 2nd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 2014)

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S. P. Dinh General DC Programming Let X = Rn and . e. not identically equal to +∞) convex functions defined on X and taking values in R ∪ {+∞}. The dual space of X denotes by Y which could be identified with X itself. For θ ∈ Γ0 (X), the effective domain of θ, denoted dom θ, is defined by dom θ := {x ∈ X : θ(x) < +∞}. (16) DC programming investigates the structure of the vector space DC(X) := Γ0 (X) − Γ0 (X), DC duality and optimality conditions for DC programs. A general DC program is in the form of (Pdc ) α = inf{f (x) := g(x) − h(x) : x ∈ X}, (17) with g, h ∈ Γ0 (X).

Let x∞ be a limit point of the sequence {xk }, say, limi→∞ xki = x∞ for some subsequence {xki } of {xk }. We prove that there exists an index k0 such that βk = βk0 for all k ≥ k0 . e, limk→∞ βk = +∞. Then, there exist infinitely many indices i such that βki < xki +1 − xki −1 as well as p(xki ) > 0; p(xki +1 ) > 0. DC Programming and DCA for General DC Programs 27 By considering a subsequence if necessarily, without loss of generality, we can assume that lim xki +1 − xki = 0 i→∞ and p(xki ) > 0; p(xki +1 ) > 0 for all i.

Moreover, a hybrid method combining DCA with an adaptive Branch and Bound is established for guaranteeing the feasibility of the BMI and QMI. A concept of partial solution of SDP via DCA is proposed to improve the convergence of our algorithm when handling more large-scale cases. Numerical simulations of the proposed approaches and comparison with PENBMI are also reported. Keywords: BMI/QMI, DC program, DCA, Branch and Bound, SDP. 1 Introduction The optimization problem with Bilinear Matrix Inequality (BMI) constraints is considered as the central problem in the filed of robust control.

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