Two interior-point algorithms for a class of convex programming problems

Two Interior-Point Algorithms for a Class of Convex Programming Problems

This paper describes two algorithms for the problem of minimizing a linear function over the intersection of an aane set and a convex set which is required to be the closure of the domain of a strongly self-concordant barrier function. One algorithm is a path-following method, while the other is a primal potential-reduction method. We give bounds on the number of iterations necessary to attain ...

Trust{region Interior{point Algorithms for a Class of Nonlinear Programming Problems Trust{region Interior{point Algorithms for a Class of Nonlinear Programming Problems

Trust{Region Interior{Point Algorithms for a Class of Nonlinear Programming Problems by Lu s Nunes Vicente This thesis introduces and analyzes a family of trust{region interior{point (TRIP) reduced sequential quadratic programming (SQP) algorithms for the solution of minimization problems with nonlinear equality constraints and simple bounds on some of the variables. These nonlinear programming...

Stable Computation Of Interior Point Solutions For A Class Of Nonlinear Convex Programming Problems

Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems

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...

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...