In this paper, we use the auxiliary principle technique to study the existence of a solution of the extended general variational inequalities, which were introduced and studied by the author. Several special cases are...
详细信息
In this paper, we use the auxiliary principle technique to study the existence of a solution of the extended general variational inequalities, which were introduced and studied by the author. Several special cases are also discussed.
In this paper, we suggest and analyze a new class of three-step projection iterative methods for solving the extended general variational inequalities, which are obtained using the updating technique of the solution i...
详细信息
In this paper, we suggest and analyze a new class of three-step projection iterative methods for solving the extended general variational inequalities, which are obtained using the updating technique of the solution in conjunction with projection technique. We also consider the convergence criteria of these new iterative methods under some mild conditions. Since the extended general variational inequalities include the general variational inequalities and other related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as a refinement and improvement of the known results.
This paper deals with an axiomatic approach to certain optimality conditions for the vector nonconvex minimization problem min {g(x) - h(x): x epsilon X}, where X is an arbitrary set and g, h are functions defined on ...
详细信息
This paper deals with an axiomatic approach to certain optimality conditions for the vector nonconvex minimization problem min {g(x) - h(x): x epsilon X}, where X is an arbitrary set and g, h are functions defined on X with values in an ordered topological vector space Z.
In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and are-connected convex functions. It is shown that the minim...
详细信息
In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and are-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm.
We establish a necessary and sufficient condition for the minima of the difference of an arbitrary function and a lower semicontinuous function defined in a metric space.
We establish a necessary and sufficient condition for the minima of the difference of an arbitrary function and a lower semicontinuous function defined in a metric space.
In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship bet...
详细信息
In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipschitz functions that are integrable, D-representable and possess desirable differentiability properties. We also present some striking applications of our results to distance functions. (C) 1997 Academic Press.
暂无评论