This paper provides another derivation of the Karmarkar direction for linear programming. It is strongly motivated by derivations of Gonzaga, but we show how the direction can be viewed as a steepest descent direction in the original feasible region corresponding to a metric diierent from the Euclidean one. We show that a xed decrease in the potential function can be obtained by taking a step i...

We present a pivoting algorithm for solving linear programs with linear complementarity constraints. Our method generalizes the simplex method for linear programming to deal with complementarity conditions. We develop an anticycling scheme that can verify Bouligand stationarity. We also give an optimizationbased technique to find an initial feasible vertex. Starting with a feasible vertex, our ...

In this paper, we present a full Newton step feasible interior-pointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the Nesterov-Todd scalingscheme, and only full-Newton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered “non serious”, a cutting plane is added and a new search direction is comput...

We present a primal-dual interior point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter ρ in the merit function i...

We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) J. Herskovits, for solving large-scale linear programs. At each step, solution two systems with same coefficient matrix is determined. This step involves a significant computational effort. Reducing time is, therefore, way to improve performance method. The be solved are associated definite positive symmetric m...

Article history: Received 9 July 2014 Accepted 19 August 2014 Available online xxxx

Article history: Received 30 October 2009 Received in revised form 17 October 2010 Accepted 12 November 2010 Available online 19 November 2010

A Fault-Tolerant Control (FTC) methodology has been presented for nonlinear processes being imposed by control input constraints. The proposed methodology uses a combination of Feedback Linearization and Model Predictive Control (FLMPC) schemes. The resulting constraints in the transformed process will be dependent on the actual evolving states, making their incorporation in the de...