Constrained nonlinear programming problems often arise in many engineering applications. The most well-known optimization methods for solving these problems are sequential quadratic programming methods and generalized reduced gradient methods. This study compares the performance of these methods with the genetic algorithms which gained popularity in recent years due to advantages in speed and r...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

Solution stability of a class of linear generalized equations in finite dimensional Euclidean spaces is investigated by means of generalized differentiation. Exact formulas for the Fréchet and the Mordukhovich coderivatives of the normal cone mappings of perturbed Euclidean balls are obtained. Necessary and sufficient conditions for the local Lipschitz-like property of the solution maps of such...

These are the basic thoughts that should go into the preface. It is not a final version. In a series of papers in the mid-1960's, Landin expounded two important observations about programming languages. First, he argued that all programming languages share a basic set of facilities for specifying computation but differ in their choice of data and data primitives. The set of common facilities co...

The lambda calculus is a formal symbolic term rewrite system that has been used for many years both as a mechanism for defining the semantics of programming languages, and as the basis for functional programming languages. In this paper, we describe a completely visual representation for lambda expressions, VEX, that has several advantages over traditional textual lambda calculus. Although VEX ...

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

ion operator; this is because [x]M is an abbreviation for a term in which M and its subterms do not occur. On the other hand, in the natural reduction for lambda-calculus, replacements inside the scope of an abstraction are extremely natural. Thus, what is now called λβ -reduction satisfies a scheme which weak reduction does not, namely (ξ): if M reduces to N, then λx.M reduces to λx.N. (The sa...

This paper presents a branch-and-bound algorithm for globally solving a wide class of generalized linear fractional programming problems (GLFP). This class includes such problems as: minimizing a sum, or error for product of a finite number of ratios of linear functions, linear multiplicative programming, polynomial programming, etc. – over nonconvex feasible region. First a problem (Q) is deri...