This note corrects a certain inaccuracy in the discussion of the projective transformation employed by Karmarkar in the reduction of a general linear programming to the form required for his algorithm In his famous paper Karmarkar proposes on page Step a reduction of a general problem to one on a subset of the unit simplex as follows Given a linear programming problemof the form Minimize cx sub...

This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solving nonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkar idea and linearization of the objective function.The second and third algorithms are modification of the first algorithm using the Schrijver andMalek-Naseri approaches, respectively. T...

The paper presents three types of extensions: venical, horizontal, and two-dimensional to the new, Faddeev algorithm based, systolic architecture for mamx computations, presented in: H.VD. Le, M A . Perkowski. ”A New General Purpose Sysrolic Archirecrure for Matrix Computationr”. Proc. Intern. Con$ on Computing and Information, ICC1’89, Ontario, Canada, 1989. It has essential advantages over pr...

The present work deals with the comparison of in vitro dissolution profiles of fenofibrate liquisolid tablet formulations with those of marketed fenofibrate tablets, and the application of statistical methods to evaluate each method for its usefulness. The methods used to study dissolution profile comparison include Model independent method (Similarity factor, f2); Model dependent methods (Zero...

Interior point methods were widely used in the past in the form of barrier methods. In linear programming, the simplex method dominated, mainly due to inefficiencies of barrier methods. Interior point methods became quit popular again after 1984, when Karmarkar announced a fast polynomial-time interior method for nonlinear programming [Karmarkar, 1984]. In this section we present primal-dual in...

We illustrate the use of phase transition behavior in the study of heuristics. Using an “annealed” theory, we define a parameter that measures the “constrainedness” of an ensemble of number partitioning problems. We identify a phase transition at a critical value of constrainedness. We then show that constrainedness can be used to analyze and compare algorithms and heuristics for number partiti...