# Advanced courses of mathematical analysis II: proceedings of by M. V. Velasco, A. Rodriguez-Palacios

By M. V. Velasco, A. Rodriguez-Palacios

This quantity includes a suite of articles by way of major researchers in mathematical research. It offers the reader with an in depth assessment of recent instructions and advances in themes for present and destiny examine within the box.

**Read or Download Advanced courses of mathematical analysis II: proceedings of the 2nd international school, Granada, Spain, 20-24 September 2004 PDF**

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**Extra resources for Advanced courses of mathematical analysis II: proceedings of the 2nd international school, Granada, Spain, 20-24 September 2004**

**Example text**

As the investor considers the expected beneﬁts constraint more important than the remaining constraints, one can consider the risk as a soft constraint, with a non-linear membership function. Le´on, Liern and Vercher calculate the tolerances analogously in Step 2 (it is not exactly the same because in this case we have a non-linear constraint). 2. 112 8 Frstn. 3. 279 655 They add to (PI) the following constraint: V (x) + h∗ = DS, where V (x) = n n σ˜ij xi xj , h∗ is a non-negative slack variable.

P3-9) and (P3-10) are linear programming problems. A few linear programming algorithms, for example, the simplex method, can be used to solve it eﬃciently. 5 Numerical Example Chinese securities markets comprise the Shanghai Stock Exchange, the Shenzhen Stock Exchange, the Hong Kong Stock Exchange and the Taipei Stock Exchange. In this section, we give an example to illustrate the model for portfolio selection proposed in this chapter. We suppose that an investor wants to choose twelve diﬀerent types of stocks and a kind of risk-less asset from the Shanghai Stock Exchange for his investment.

Assume that m1 greater or equal type ˜2 , · · · , B ˜m , m2 less or equal type fuzzy constraints ˜1 , B fuzzy constraints B 1 52 5 Le´ on-Liern-Vercher’s Model C˜1 , C˜2 , · · · , C˜m2 , mi ≤ pi (i = 1, 2). Denote by µB˜i (x) and µC˜i (x) the mem˜i and C˜i , respectively. 1 Deﬁne the fuzzy set of feasible solutions of P E {(x, µE˜ (x)), x ∈ X}, where µE˜ (x) µE˜ (x) = min{µB˜1 (x), · · · , µB˜m (x), µC˜1 (x), · · · , µC˜m (x)}. 1 2 ˜ is non-empty, so the following fuzzy program Notice that the fuzzy set E is consistent: (FP) ﬁnd {x ∈ X : A1 x ≥ b1 , A2 ≤ b2 }.