In this study, we firstly express the stochastic user equilibrium traffic assignment problem in asymmetric traffic network as variation inequality model and then formulate ntinuous network design problem as mathematical program with equilibrium constraints. When path flow travel cost function is continuous, differentiable and strong monotone, the solution of variational inequality follows logit...

In this paper, we try to solve the semidefinite program with box constraints. Since the traditional projection method for constrained optimization with box constraints is not suitable to the semidefinite constraints, we present a new algorithm based on the feasible directionmethod. In the paper, we discuss two cases: the objective function in semidefinite programming is linear and nonlinear, re...

Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper, we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines the traditional c...

In this paper we present a new feasible direction method to find all efficient extreme points for bi criterion linear fractional programming problems. This method is based on the conjugate gradient projection method. An initial feasible point is used to generate all efficient extreme points for this problem through a sequence of feasible directions of movement. Since methods based on vertex inf...

Semismooth Newton methods constitute a major research area for solving mixed complementarity problems (MCPs). Early research on semismooth Newton methods is mainly on infeasible methods. However, some MCPs are not well defined outside the feasible region or the equivalent unconstrained reformulations of other MCPs contain local minimizers outside the feasible region. As both these problems coul...

We present a new algorithm for nonlinear semidefinite programming, based on the iterative solution in the primal and dual variables of Karush-KuhnTucker optimality conditions, which generates a feasible decreasing sequence. At each iteration, two linear systems with the same matrix are solved to compute a feasible descent direction and then an inexact line search is performed in order to determ...

This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0–1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounde...

This paper explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions f at a given point, it is shown that for quadratic functions there exists exactly one invariant descent direction in the strictly convex case and generally none in the nondegenerate indefinite case. These ...