In this paper we derive new farfield boundary conditions for the timedependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditio...

An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described It applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives This framework permits primal and primal dual steps but the paper focuses on the ...

This thesis aims to introduce and analyse a primal-dual active set strategy for solving Allen-Cahn variational inequalities. We consider the standard Allen-Cahn equation with non-local constraints and a vector-valued Allen-Cahn equation with and without non-local constraints. Existence and uniqueness results are derived in a formulation involving Lagrange multipliers for local and non-local con...

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007...

Given a limited resource (such as bandwidth or memory) we consider the problem of scheduling requests from clients that are given as groups of non-intersecting time intervals. Each request j is associated with a demand (the amount of resource required), dj , a t-interval , which consists of up to t segments, for some t ≥ 1, and a weight, w(j). A schedule is a collection of requests. It is feasi...

We consider a class of augmented Lagrangian methods for solving convex programming problems with inequality constraints. This class involves a family of penalty functions and specific values of parameters p, q, ỹ ∈ R and c > 0. The penalty family includes the classical modified barrier and the exponential function. The associated proximal method for solving the dual problem is also considered. ...

In this paper we deal with the minimization of a convex function over the solution set of a range inclusion problem determined by a multivalued operator with convex graph. We attach a dual problem to it, provide regularity conditions guaranteeing strong duality and derive for the resulting primal-dual pair necessary and sufficient optimality conditions. We also discuss the existence of optimal ...

Linear programming (LP) is an important field of optimization. Even though, interior point methods are polynomial algorithms, many LP practical problems are solved more efficiently by the primal and dual revised simplex methods (RSM); however, RSM has a poor performance in hard LP problems (HLPP) as in the Klee-Minty Cubes problem. Among LP methods, the hybrid method known as Simplex-Genetic (S...

We consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form. By characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems, we show that these trajectories tend to an optimal solution which in general depends on the starting point. By con...

We generalize the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhu and Chan in [M. Zhu, and T. F. Chan, An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration, UCLA CAM Report [08-34], May 2008] to a broader class of convex optimization problems. In addition, we survey several closely related methods and explain the connections to PDHG. We point out...