A new polynomial-time algorithm for linear programming
Combinatorica
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
A polynomial-time algorithm, based on Newton's method, for linear programming
Mathematical Programming: Series A and B
Interior algorithms for linear, quadratic, and linearly constrained convex programming
Interior algorithms for linear, quadratic, and linearly constrained convex programming
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In this article we propose a polynomial-time algorithm for linear programming. This algorithm augments the objective by a logarithmic penalty function and then solves a sequence of quadratic approximations of this program. This algorithm has a complexity of O(m^1^2 L) iterations and O(m^3^.^5L) arithmetic operations, where m is the number of variables and L is the size of the problem encoding in binary. The novel feature of this algorithm is that it admits a very simple proof of its complexity, which makes it valuable both as a teaching and as a research tool. Moreover, its convergence can be accelerated by performing a line search and the line search stepsize is obtainable in a closed form. This algorithm maintains primal and dual feasibility at all iterations.