Issue 2, Volume 25, August 2000

2000 · Open access

1. ON NECESSARY OPTIMALITY CONDITIONS IN MULTIFUNCTION OPTIMIZATION WITH PARAMETERS PHAN QUOC KHANH, LE MINH LUU PDF

   ▸ Abstract

   We consider multifunction optimization problems with parameters. Necessary optimality conditions of the Fritz John and Kuhn-Tucker types are obtained with relaxed differentiability assumptions on the state variable and convexlikeness assumptions on the parameter.

   125-136
2. PROPRIÉTÉS SPECTRALES LOCALES D'UNE MATRICE CARRÉE DES OPÉRATEURS M. HOUIMDI, H. ZGUITTI PDF

   ▸ Abstract

   If $X$ and $Y$ are complex Banach spaces, then for $A\in\mathcal L(X)$, $B\in\mathcal L(Y)$ and $C\in\mathcal L(Y,X)$ we denote by $M_C$ the operator defined on $X\oplus Y$ by
   $$ M_C=\begin{pmatrix} A&C\\ 0&B \end{pmatrix}.$$
   When $B$ has SV EP, we show that $\sigma(M_C)=\sigma(A)\cup\sigma(B)$ for all $C\in\mathcal L(Y,X)$. And in the Hilbert space setting, this result gives a partial positive answer to the question 3 posed in [5].

   137-144
3. ON THE EXISTENCE OF BOUNDED SOLUTIONS FOR LOTKA-VOLTERRA EQUATIONS NGUYEN HUU DU PDF

   ▸ Abstract

   This article deals with an extension of Ahmad's results in studying the existence and uniqueness of a solution bounded above and below by positive constants by mean of weakening the conditions imposed on the coe±cients of competing species equations of random Lotka-Volterra type.

   145-159
4. RATE OF CONVERGENCE IN BOOTSTRAP APPROXIMATIONS WITH RANDOM SAMPLE SIZE NGUYEN VAN TOAN PDF

   ▸ Abstract

   We give the convergence rates of the random sample size bootstrap approximations of the distribution of the sample mean. Using the quantity $\alpha^2_n=E[(\frac{N_n}{n}-1)^2]$, where $N_n$ is the random sample size, we obtain a convergence rate $O(n^{-\frac 12}(\log\log n)^{\frac 12})$ if $\alpha_n=O(n^{-\frac 12}(\log\log n)^{\frac 12})$.

   161-179
5. AN INVARIANT PROPERTY OF INVEX FUNCTIONS AND APPLICATIONS DO VAN LUU, NGUYEN XUAN HA PDF

   ▸ Abstract

   Under directional differentiability assumptions, we prove that the minimum or the maximum of a finite family of invex functions is again an invex function. This invariant property of the invex functions is used to obtain first-order optimality conditions for a class of optimization problems.

   181-193
6. SOME COLLECTIONS OF FUNCTIONS DENSE IN AN ORLICZ SPACE TRUONG VAN THUONG PDF

   ▸ Abstract

   This paper presents sufficient conditions for a translation invariant subspace of $L_1(\mathbb R^n)\cap L_{\Phi}(\mathbb R^n)$ to be dense in the Orlicz space $L_{\Phi}(\mathbb R^n)$.

   195-208
7. STRONG POLYNOMIAL-TIME SOLVABILITY OF A MINIMUM CONCAVE COST NETWORK FLOW PROBLEM HOANG TUY PDF

   ▸ Abstract

   A new simple proof is given of the strong polynomial-time solvability of the single source uncapacitated minimum concave cost network flow problem (SSUMCCNFP) with a fixed number of nonlinear arc costs.

   209-217
8. DEFICIENCIES OF COMPOSITE ENTIRE FUNCTIONS JIANWU SUN PDF

   ▸ Abstract

   In this paper we generalize a result of Goldstein.

   219-229
9. LYAPUNOV STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS TRAN TIN KIET, VU NGOC PHAT PDF

   ▸ Abstract

   The paper studies asymptotic stability of nolinear time-varying differential equations by Lyapunov's direct method. Sufficient conditions for asymptotic stability are given in terms of nondifferentiable Lyapunov-like functions. An application to stabilizability of a class of nonlinear control systems with feedback controls is also given.

   231-249