Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems...

cSpackman, D. H., W. H. Stein, and S. Moore, Anal. Chem., 30, 1190 (1958). 6Karush, F., and R. Marks, J. Immunol., 78, 296 (1957). 7Koshland, M. E., F. M. Englberger, and S. M. Gaddone, J. Immunol., 89, 517 (1962). 8 Eisen, H. N., and F. Karush, J. Am. Chem. Soc., 71, 363 (1949). 9 Karush, F., J. Am. Chem. Soc., 78, 5519 (1956). 10 The anti-p-azobenzenearsonic acid antibody will be referred to ...

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...

A novel model including social, environmental and economic benefits is proposed in hybrid thermal/wind power system and studied by Karush-Kuhn-Tucker and hybrid particle swarm optimization techniques. Our work is the first to develop social dispatch model by calculating risk caused by wind power. Then the novel multi-objective optimization model of social-environment-economic dispatch is establ...

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications introduce a weak qualification which assures the equivalence between SCAKKT Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483-500, 1994) problems.

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

The main purpose of these lectures is to familiarize the student with the basic ingredients of convex analysis, especially its subdifferential calculus. This is done while moving to a clearly discernible end-goal, the Karush-Kuhn-Tucker theorem, which is one of the main results of nonlinear programming. Of course, in the present lectures we have to limit ourselves most of the time to the Karush...

In this paper we analyze the application of Newton's method to the solution of systems of nonlinear equations arising from equivalent forms of the rst{order Karush{Kuhn{Tucker necessary conditions for constrained optimization. The analysis is carried out by using an abstract model for the original system of nonlinear equations and for an equivalent form of this system obtained by a reformulatio...