A new polynomial-time algorithm for linear programming
Combinatorica
A polynomial-time algorithm, based on Newton's method, for linear programming
Mathematical Programming: Series A and B
Modified barrier functions (theory and methods)
Mathematical Programming: Series A and B
A primal-dual infeasible-interior-point algorithm for linear programming
Mathematical Programming: Series A and B
On the convergence of the exponential multiplier method for convex programming
Mathematical Programming: Series A and B
A deep cut ellipsoid algorithm for convex programming: theory and applications
Mathematical Programming: Series A and B
On the entropic perturbation and exponential penalty methods for linear programming
Journal of Optimization Theory and Applications
Nonlinear rescaling and proximal-like methods in convex optimization
Mathematical Programming: Series A and B
Computational Optimization and Applications - Special issue on nonsmooth and smoothing methods
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Complexity of a noninterior path-following method for the linear complementarity problem
Journal of Optimization Theory and Applications
A Globally and Locally Superlinearly Convergent Non--Interior-Point Algorithm for P0 LCPs
SIAM Journal on Optimization
Convex Optimization
Numerical Experiments with an Interior-Exterior Point Method for Nonlinear Programming
Computational Optimization and Applications
Primal-dual nonlinear rescaling method with dynamic scaling parameter update
Mathematical Programming: Series A and B
A Full-Newton Step O(n) Infeasible Interior-Point Algorithm for Linear Optimization
SIAM Journal on Optimization
The Complexity of Self-Regular Proximity Based Infeasible IPMs
Computational Optimization and Applications
Self-concordant functions for optimization on smooth manifolds
Journal of Global Optimization
1.5-Q-superlinear convergence of an exterior-point method for constrained optimization
Journal of Global Optimization
Simplified O(nL) infeasible interior-point algorithm for linear optimization using full-Newton steps
Optimization Methods & Software
Primal-dual exterior point method for convex optimization
Optimization Methods & Software
A Primal-Dual Exterior Point Method for Nonlinear Optimization
SIAM Journal on Optimization
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We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form can be converted into an unconstrained optimization problem. The relevant properties on the unconstrained optimization problem such as the duality, the boundedness of the solution and the path-following lemma, etc, are proved. Second, a self-concordant function on entire space which can be used as penalty for linear programming is constructed. For this specific function, more results are obtained. In particular, we show that, by taking a parameter large enough, the optimal solution for the unconstrained optimization problem is located in the increasing interval of the self-concordant function, which ensures the feasibility of solutions. Then by means of the self-concordant penalty function on entire space, a path-following algorithm on entire space for linear programming is presented. The number of Newton steps of the algorithm is no more than $$O(nL\log (nL/ {\varepsilon }))$$, and moreover, in short step, it is no more than $$O(\sqrt{n}\log (nL/{\varepsilon }))$$.