Download Advanced Computational Methods for Knowledge Engineering by Nguyen Van Thoai (auth.), Ngoc Thanh Nguyen, Tien van Do, PDF

By Nguyen Van Thoai (auth.), Ngoc Thanh Nguyen, Tien van Do, Hoai An le Thi (eds.)

The e-book includes 29 prolonged chapters that have been chosen and invited from the submissions to the 1st foreign convention on laptop technology, utilized arithmetic and Applications (ICCSAMA 2013) hung on 9-10 may well, 2013 in Warsaw, Poland. The publication is geared up into 5 components, that are: complicated Optimization equipment and Their purposes, Queuing conception and functions, Computational tools for wisdom Engineering, wisdom Engineering with Cloud and Grid Computing, and common sense established equipment for selection Making and information Mining, respectively. All chapters within the e-book speak about theoretical and functional concerns hooked up with computational equipment and optimization equipment for wisdom engineering.

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Q=1 Then it holds that (a) lim μk = lim f (xk ) = lim γk , and k→∞ k→∞ k→∞ (b) Every accumulation point x∗ of the sequence {xk } is a global optimal solution of Problem (7). Proof. (a) Let x∗ be an accumulation point of the sequence {xk } ⊂ S 1 ∩ D, and let f ∗ be the optimal value of Problem (7). Since the sequence {μk } of lower bounds is computed by (20), it is monotonically nondecreasing and bounded from above by f ∗ . Moreover, the sequence {γk } of upper bounds is nonincreasing and Algorithm for IPH Optimization Problems 27 bounded from below by f ∗ .

The authors claimed that their heuristic method for solving the former model can be adapted to solve the later. T. Nguyen, T. A. ): ICCSAMA 2013, SCI 479, pp. 31–40. 1007/978-3-319-00293-4_3 32 P. A. D. Tao The starting point of our work is the second model introduced in [8]. We consider a little modified model where the constraints include shortselling constraints, limit on expected return, limit on variance, and diversification constraints. The considered transaction cost is assumed to be separable, say the sum of the transaction cost associated with each trade.

Since the sequence {μk } of lower bounds is computed by (20), it is monotonically nondecreasing and bounded from above by f ∗ . Moreover, the sequence {γk } of upper bounds is nonincreasing and Algorithm for IPH Optimization Problems 27 bounded from below by f ∗ . Therefore, μ∗ = lim μk and γ ∗ = lim γk exist, k→∞ and, because of γk = f (xk ) and continuity of f (x), we obtain k→∞ lim μk = μ∗ ≤ f ∗ ≤ γ ∗ = lim γk = lim f (xk ) = f (x∗ ). k→∞ k→∞ k→∞ (21) Now, let {xq } be a subsequence of {xk } which converges to x∗ .

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