Zhongyi Liu

A full-Newton step infeasible interior-point algorithm for linear programming based on a kernel function

  • Zhongyi Liu
    • Categories Convex Optimization, Linear Programming Tags , , , ,

    This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110–1136, 2006). We introduce a kernel function in the algorithm. For $p\in[0,1)$, the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, … Read more

    A globally convergent primal-dual interior-point 3D filter method for nonlinear SDP

  • Zhongyi Liu
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , ,

    This paper proposes a primal-dual interior-point filter method for nonlinear semidefinite programming, which is the first multidimensional (three-dimensional) filter methods for interior-point methods, and of course for constrained optimization. A freshly new definition of filter entries is proposed, which is greatly different from those in all the current filter methods. A mixed norm is used … Read more