Generalized semi-infinite optimization problems (GSIP) are considered. It is investigated how the numerical methods for standard semi-infinite programming (SIP) can be extended to GSIP. Newton methods can be extended immediately. For discretization methods the situation is more complicated. These difficulties are discussed and convergence results for a discretizationand an exchange method are d...

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In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that σ f = 22n+s for every s-plateaued generalized Boolean function in n variables. Two classes of generalized semi-...

In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do ...

In this article, a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function is presented. It is demonstrated for every s-plateaued generalized Boolean function in n variables that σ f = 22n+s. Two constructions on generalized semi-bent Boolean functions are presented. A class of generalized semi-bent functions in ...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...