The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints...

In this paper a symmetric primal-dual transformation for positive semideenite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primal-dual transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newt...

Buffering of H+ and OHions in pure water probably represent the most primal physicochemical buffering phenomena, and their quantitative description is of great interest. In this context, “pure water” shall mean water without any solutes that could act as H+ buffers. In the following, it is understood that addition of H+ ions to pure water, or removal of H+ ions from it is carried out in the for...

A discussion of duality continues the development of a mathematical theory for bond graphs as combinatorial structures. The dual of a bondgraph is de$ned and its associated vector spaces are the co-spaces of the original bond graph. The relationship between the algebraic structures and their duals is explored. The theory is used to justfy the construction of a simplified bond graph, the proper ...

We introduce and study the primal-dual exterior point (PDEP) method for convex optimization problems. The PDEP is based on the Nonlinear Rescaling (NR) multipliers method with dynamic scaling parameters update. The NR method at each step alternates finding the unconstrained minimizer of the Lagrangian for the equivalent problem with both Lagrange multipliers and scaling parameters vectors updat...

Received: date / Revised version: date Abstract. A class Ψ of strongly concave and smooth functions ψ : R → R with specific properties is used to transform the terms of the classical Lagrangian associated with the constraints. The transformation is scaled by a positive vector of scaling parameters, one for each constraint. Each step of the Lagrangian Transformation (LT) method alternates uncons...

The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

This paper describes several methods for solving nonlinear complementarity problems. A general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem, obtaining primal, dual, and primal-dual formulations. We derive Bregman-function-based generalized proximal algorithms for each of these formulations, generating three classes of co...

We develop a primal dual active set with continuation algorithm for solving the l-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates...