10 Optimality Conditions for CDTSubproblemXiongda
نویسندگان
چکیده
In this paper, we give necessary and suucient optimality conditions which are easy veriied for the local solution of Celis-Dennis-Tapia sub-problem (CDT subproblem) where the Hessian at this local solution has one negative eigenvalue. If CDT subproblem has no global solution with Hessian of Lagrangian positive semi-deenite, the Hessian of Lagrangian has at least one negative eigenvalue. It is very important to investigate all the stationary points of Lagrangian dual function and to characterize the local solutions. We also discuss the gap between these two conditions.
منابع مشابه
On Sequential Optimality Conditions without Constraint Qualifications for Nonlinear Programming with Nonsmooth Convex Objective Functions
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...
متن کاملSufficient global optimality conditions for general mixed integer nonlinear programming problems
In this paper, some KKT type sufficient global optimality conditions for general mixed integer nonlinear programming problems with equality and inequality constraints (MINPP) are established. We achieve this by employing a Lagrange function for MINPP. In addition, verifiable sufficient global optimality conditions for general mixed integer quadratic programming problems are der...
متن کاملOptimality conditions for Pareto efficiency and proper ideal point in set-valued nonsmooth vector optimization using contingent cone
In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.
متن کاملSequential Optimality Conditions and Variational Inequalities
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 ...
متن کاملOn Optimality Conditions via Weak Subdifferential and Augmented Normal Cone
In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997