A new initialization or ‘Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path — our initial method (Algo...

In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method ...

the verse on “the world of primal covenant (‘alam al-zarr)” is among difficult quranic verses whose difficulty can be discovered by consideration of different opinions, which are sometimes opposite to one another, presented by quranic commentators. having accepted the existence of “the world of primal covenant,” mulla sadra has interpreted and expounded that world in accordance with his philoso...

We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm, and then transforming it into a primal-dual algorithm. This was done in the case of the 2-approximation algorithms for the f...

In this paper, we give a recursive formula for optimal dual barrier functions on homogeneous cones. This is done in a way similar to the primal construction of Güler and Tunçel [1] by means of the dual Siegel cone construction of Rothaus [2]. We use invariance of the primal barrier function with respect to a transitive subgroup of automorphisms and the properties of the duality mapping, which i...

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

Propositional primal logic, as defined by Gurevich and Neeman, has two kinds of quotations: p said φ, and p implied φ. Note 1. The derivation problem for propositional primal logic with one kind of quotations is solvable linear time. Note 2. In the Hilbertian calculus for propositional primal logic, the shortest derivation of a formula φ from hypotheses H may be exponential in the length of (H,φ).

In this paper we propose two new nonsymmetric primal-dual potential-reduction methods for conic problems. The methods are based on the primal-dual lifting [5]. This procedure allows to construct a strictly feasible primal-dual pair related by an exact scaling relation even if the cones are not symmetric. It is important that all necessary elements of our methods can be obtained from the standar...

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...