First and second order conditions for a class of nondifferentiable optimization problems

Continuous programming containing arbitrary norms

“…These duality results generalize some results of Abrham and Buie [2] for the differentiable case and give a dynamic analogue of certain nondifferentiable fractional programming problems considered by Mond [20]. They also give duality results to the fractional analogues of problems considered by Watson [32], Fletcher and Watson [18], which have not been studied explicitly in the literature.…”

“…The results of this paper also give duals to the (static) mathematical programming problems of Fletcher and Watson [18] (and some of its variants), which have not been reported in the literature explicitly. As a special case of this, we get the duality results of Mond [2], Mond and Schechter [23] and Watson [32].…”

“…The pair (P2)-(D2) could also be considered as an extension of Schechter [31] with regard to the converse duality, because in [31], it is given for differentiable constraints only. Also by taking m = 1, S = R + , g(x) = -8, (S > 0) (P2) reduces to the problem of Fletcher and Watson [18], who give optimality conditions only and do not discuss duality.…”

Majorizing Functions and Convergence of the Gauss–Newton Method for Convex Composite Optimization

“…As observed by Burke and Ferris in their seminal paper [4], a wide variety of its applications can be found throughout the mathematical programming literature especially in convex inclusion, minimax problems, penalization methods and goal programming, see also [2,6,7,15,22]; the study of (1.1) not only provides a unifying framework for the development and analysis of algorithmic for solutions but also a convenient tool for the study of first-and second-order optimality conditions in constrained optimization [3,5,7,22]. As in [4,13], the study of (1.1) naturally relates to the convex inclusion problem…”

On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization

“…Computation of the secondorder correction term is costly, so we only try d SOC if the step d k has been rejected, x k is already nearly feasible, and v k is small compared with Z k u k . These conditions attempt to identify the occurrence of the Maratos effect and are much simpler than the rules given by Fletcher [19]. Combining this with the ideas of section 4.6, the final if statement of Algorithm 2.1 is more precisely defined by the following rules.…”