We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This has two names in literature: Primal-Dual Fixed-Point based on the Proximity Operator (PDFP$^2$O) Proximal Alternating Predictor-Corrector (PAPC). In this paper, we prove its convergence under weaker condition stepsizes than existing ones. With additional assumptions, show l...

In this article, the authors present a new Lp-primal–dual weak Galerkin method (Lp-PDWG) for convection–diffusion equations. Comparing with standard L2-PDWG method, solution calculated from Lp-PDWG may exhibit some important advantages and features (e.g., less jumps cross element interface when p?1, or sparsity by using p=1 wavelet basis approximation). The existence uniqueness of numerical is ...

An approach to determine primal and dual stepsizes in the infeasible{ interior{point primal{dual method for convex quadratic problems is presented. The approach reduces the primal and dual infeasibilities in each step and allows diierent stepsizes. The method is derived by investigating the eecient set of a multiobjective optimization problem. Computational results are also given.

We consider a Primal-Dual Augmented Lagrangian (PDAL) method for optimization problems with equality constraints. Each step of the PDAL requires solving the Primal-Dual linear system of equations. We show that under the standard second-order optimality condition the PDAL method generates a sequence, which locally converges to the primal-dual solution with quadratic rate.

Iterative substructuring methods with Lagrange multipliers for the elliptic system of linear elasticity are considered. The algorithms belong to the family of dual-primal FETI methods which was introduced for linear elasticity problems in the plane by Farhat et al. [2001] and then extended to three dimensional elasticity problems by Farhat et al. [2000]. In dual-primal FETI methods, some contin...

A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their corresponding primal edges. The problem of constructing such drawings has a long tradition when the drawings of both primal and dual are required to be straight-...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗(κ) linear complementarity problems (LCPs). We generalize the analysis of BER’s primal-dual interior point algorithm for LP to P∗(κ) LCPs. New search directions and proximity measures are proposed based on a new kernel function which has linear growth term. We showed that if a strictly feasible starting point...

We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set B of at most three bases, each of a different type, in each iteration: a primal feasible basis Bp, a dual feasible basis Bd and a primal-and-dual infeasible basis Bi. From each B ∈ B, it evaluates the primal and dual feasibility of all primal and dual pivots to...

In this technical report the new version of the software Dgc tool is presented. This tool allows us to build up irregular graph pyramids by dual graph contraction. The graph pyramid consists of a stack of levels (pair of graphs), each of which has a primal level and its dual. Every successive level is a reduced version of the level below. Primal level and its dual represent a primal graph and i...