A new polynomial-time algorithm for linear programming
Combinatorica
Mathematical Programming: Series A and B
A polynomial-time algorithm, based on Newton's method, for linear programming
Mathematical Programming: Series A and B
The projective SUMT method for convex programming
Mathematics of Operations Research
A primal-dual interior point algorithm for linear programming
Progress in Mathematical Programming Interior-point and related methods
Pathways to the optimal set in linear programming
on Progress in Mathematical Programming: Interior-Point and Related Methods
Interior path following primal-dual algorithms. Part I: Linear programming
Mathematical Programming: Series A and B
Interior path following primal-dual algorithms. Part II: Convex quadratic programming
Mathematical Programming: Series A and B
Mathematics of Operations Research
A combined homotopy interior point method for convex nonlinear programming
Applied Mathematics and Computation
Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem
Nonlinear Analysis: Theory, Methods & Applications
Interior Point Techniques in Optimization: Complementarity, Sensitivity and Algorithms
Interior Point Techniques in Optimization: Complementarity, Sensitivity and Algorithms
Hi-index | 7.29 |
In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solve. However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.