Necessary and sufficient condition on global optimality without convexity and second order differentiability
نویسندگان
چکیده
منابع مشابه
Necessary and sufficient condition on global optimality without convexity and second order differentiability
The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function and its bidual (the latter is known from convex analysis).
متن کاملSecond Order Necessary and Sufficient Optimality Conditions under Abstract Constraints
In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order suucient conditions. We show tha...
متن کاملA necessary second-order optimality condition in nonsmooth mathematical programming
Generalized second–order directional derivatives for nonsmooth real–valued functions are studied and their connections with second–order variational sets are investigated. A necessary second–order optimality condition for problems with inequality constraints is obtained.
متن کاملGlobal Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition
In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems with quadratic equality and bivalent constraints. Then, we examine situations where this optimality condition is equivalent to checking the po...
متن کاملSecond-Order Necessary and Sufficient Optimality Conditions for Optimization Problems and Applications to Control Theory
This paper deals with a class of nonlinear optimization problems in a function space, where the solution is restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type. Second-order necessary and sufficient optimality conditions are established, where the cone of critical directions is arbitrarily close to the form which is expected...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Optimization Letters
سال: 2012
ISSN: 1862-4472,1862-4480
DOI: 10.1007/s11590-012-0465-9