In this paper, we present an interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which we propose a generalization of the work of Kheirfam and Nasrollahi \cite{kheirfam2018full}, that consists in determining the descent directions through a parametric algebraic transformation. The work concludes with a complete study of the convergence of the algorithm and its complexity, where we show that the obtained algorithm achieves a polynomial complexity bounds.

翻译：本文提出一种用于求解线性约束凸优化问题的全牛顿步内点算法，该算法通过参数代数变换确定下降方向，推广了Kheirfam与Nasrollahi的工作\cite{kheirfam2018full}。文中完成了算法收敛性及复杂性的完整研究，表明所提算法具有多项式复杂性界。