A fast Newton method is proposed for solving linear programs with a very large (≈ 10) number of constraints and a moderate (≈ 10) number of variables. Such linear programs occur in data mining and machine learning. The proposed method is based on the apparently overlooked fact that the dual of an asymptotic exterior penalty formulation of a linear program provides an exact least 2-norm solution...

Abstract In this paper we have investigated a fuzzy linear programming problem with fuzzy quantities which are LR triangular fuzzy numbers. The given linear programming problem is rearranged according to the satisfactory level of constraints using breaking point method. By considering the constraints, the arranged problem has been investigated for all optimal solutions connected with satisf...

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respe...

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method.

In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal objective function we propose two distributed dual fast gradient schemes for which we prove sublinear rate of convergence for dual suboptimality but also primal subo...

23] C.L. Monma and A.J. Morton. Computational experimental with a dual aane variant of Karmarkar's method for linear programming. extension of Karmarkar type algorithm to a class of convex separable programming problems with global linear rate of convergence. Techni-28] J. Renegar. A polynomial-time algorithm based on Newton's method for linear programming. Implementing an interior point method...

We propose an extension of primal grammars (Hermann & Galbavý 1997). Primal grammars are term grammars with a high expressive power and good computational properties. The extended grammars have exactly the same properties but are more modular, more concise, and easier to use, as shown by some examples. An algorithm transforming any extended primal grammar into an equivalent primal grammar is pr...

Many interior-point methods for linear programming are based on the properties of the logarithmic barrier function. After a preliminary discussion of the convergence of the (primal) projected Newton barrier method, three types of barrier method are analyzed. These methods may be categorized as primal, dual and primal-dual, and may be derived from the application of Newton’s method to different ...

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...