This paper proposes an efficient and accurate forecasting algorithm for the MDCEV model. The algorithm builds on simple, yet insightful, analytical explorations with the Kuhn-Tucker conditions of optimality that shed new light on the properties of the MDCEV model. For specific, but reasonably general, functional forms of the consumption utility specification, the algorithm circumvents the need ...

This study deals with the effects of a supply chain (SC) with single product, multiple retailers and a manufacturer, where the manufacturer(he) produces lotsize of the product that contains a random portion of imperfect quality item. The imperfect quality products are sold in a secondary shop. The new contribution of this paper is a new non-linear demand function. Demand of the end customers va...

Abstract In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient are proved for such nonconvex smooth vector optimization problems. Further, duals in sense Mond–Weir defined considered and several duality re...

Necessary and suucient conditions for optimality, in the form of a duality result of Fritz-John type, are given for an abstract optimization problem of Lyapunov type. The introduction of a so-called integrand constraint qualiication allows the duality result to take the form of a Kuhn-Tucker type result. Special applications include necessary and suucient conditions for the existence of optimal...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

The EM-ML (expectation-maximization, maximum-likelihood) algorithm for PET reconstruction is an iterative method. Sequence convergence to a fixed point that satisfies the Karush-Kuhn-Tucker conditions for optimality has previously been established [1, 2, 3]. This correspondence first gives an alternative proof of sequence convergence and optimality based on direct expansion of certain Kullback ...

Considering the minmax programming problem, lower and upper subdifferential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely different from that of most of the previous works where generalizations of the alternative theorem of Farkas have been applied. The results obtained are closed to...

The aim of this paper is to study first order optimality conditions for ideal efficient points in the Löwner partial order, when the data functions of the minimization problem are differentiable and convex with respect to the cone of symmetric semidefinite matrices. We develop two sets of first order necessary and sufficient conditions. The first one, formally very similar to the classical Karu...

The cones of directions of constancy are used to derive: new as well as known optimality conditions; weakest constraint qualifications; and regularization techniques, for the convex programming problem. In addition, the "badly behaved set" of constraints, i.e. the set of constraints which causes problems in the Kuhn-Tucker theory, is isolated and a computational procedure for checking whether a...