Abstract In this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions Wolfe type as well Mond–Weir duality theorems under semilocal E -preinvex functions. Furthermore, present saddle-point criteria to relate optimal solution programming a saddle point Lagrangian function.

The paper considers the problem of nding saddle node bifur-cation points which are closest (in a local sense) to the power system operating point. This optimization problem leads to a set of equations which describe such critical points. Not all solutions of this set of equations are critical points. The paper therefore explores the nature and characteristics of solutions. A two stage algorithm...

This paper focuses on the convergence of the modified nonlinear inexact Uzawa algorithm (MNIU) for solving the saddle point problem. We improve the sufficient conditions for convergence and the convergence rate shown in Bramble et al. [J. Bramble, J. Pasciak, and A. Vassilev, Analysis of the inexact Uzawa algorithm for saddle point problems, SIAM J. Numer. Anal., 34 (1997), pp. 1072–1092] and Y...

Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for t...

Under the notable Issacs’s condition on the Hamiltonian, the existence results of a saddle point are obtained for the stochastic recursive zero-sum differential game and mixed differential game problem, that is, the agents can also decide the optimal stopping time. Themain tools are backward stochastic differential equations BSDEs and double-barrier reflected BSDEs. As the motivation and applic...

We assume that A is n×n and C is an m×m matrix. Many such systems arise from 9 the discretization of (systems of) partial differential equations. For example, Stokes 10 equations discretized with stable finite elements or a mixed finite element method 11 for second order elliptic PDEs lead to a positive definite matrix A and to C = 0, so 12 that (1) has a genuine saddle point structure. Certain...

In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternat...

SVM wrapper feature selection method for the classification problem, introduced in our previous work [1], is analyzed. The method based on modification of the standard SVM criterion by adding to the basic objective function a third term, which directly penalizes a chosen set of variables. The criterion divides the set of all variables into three subsets: deleted, selected and weighted features....

In case f0 and C are convex, a variety of primal/dual numerical methods can be used to find the saddle points of a Lagrangian L associated with this problem [4, 7]. These methods take advantage of the fact that the search for the saddle points of L is unconstrained, or conducted over sets much simpler than C. Furthermore, we can introduce penalties on f0 in a way that regularizes L and makes it...