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We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, ). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. [ABSTRACT FROM AUTHOR]

The notion of extended-well-posedness has been introduced by Zolezzi for scalar minimization problems and has been further generalized to vector minimization problems by Huang. In this paper, we study the extended well-posedness properties of vector minimization problems in which the objective function is C-quasiconvex. To achieve this task, we first study some stability properties of such problems. [ABSTRACT FROM AUTHOR]

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved. [ABSTRACT FROM AUTHOR]

This paper develops two necessary conditions for a local minimum of an arbitrary extended real-valued function (Theorem 2.2) and, quite separately, two conditions, each sufficient for such a function to have a strict local minimum (Theorem 2.3). [ABSTRACT FROM AUTHOR]

Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded, payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value. In addition, one player possesses an ε-optimal stationary strategy ( ε>0), whereas the other has an optimal stationary strategy. [ABSTRACT FROM AUTHOR]

A mixed optimal model approximation is presented to obtain reduced-order models for truly fast descriptor systems. By a projection from truly fast descriptor systems to discrete-time systems, a mixed optimal model approximation for truly fast descriptor systems is transformed to a mixed optimal model approximation of the corresponding discrete-time systems. The structure of the fast descriptor systems is preserved in the model approximation procedure. The expression of the error and its gradient are given explicitly in terms of the solutions of certain Lyapunov equations. A numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We are concerned with a degenerate second-order identification problem in a Banach space. Suitable hypotheses on the operators involved are made in order to reduce the given problem to a nondegenerate problem. Some applications to partial differential equations are indicated extending well-known results in the regular case. [ABSTRACT FROM AUTHOR]