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Interior path following primal-dual algorithms. part I: Linear programming
TLDR
A primal-dual interior point algorithm for linear programming problems which requires a total of O(n L) number of iterations to find the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. Expand
Interior path following primal-dual algorithms
We describe a primal-dual interior point algorithm for linear programming and convex quadratic programming problems which requires a total of O(n$\sp3$L) arithmetic operations. Each iteration updatesExpand
Interior path following primal-dual algorithms. part II: Convex quadratic programming
TLDR
A primal-dual interior point algorithm for convex quadratic programming problems which requires a total of O(n3L) number of iterations, whereL is the input size. Expand
An implementation of Karmarkar's algorithm for linear programming
TLDR
Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested and compares favorably with the simplex codeMinos 4.0. Expand
A Polynomial-Time Primal-Dual Affine Scaling Algorithm for Linear and Convex Quadratic Programming and Its Power Series Extension
TLDR
An algorithm for linear and convex quadratic programming problems that uses power series approximation of the weighted barrier path that passes through the current iterate in order to find the next iterate that can be interpreted as an affine scaling algorithm in the primal-dual setup is described. Expand
Modeling and Computing Two-Settlement Oligopolistic Equilibrium in a Congested Electricity Network
TLDR
A model of two-settlement electricity markets is introduced, which accounts for flow congestion, demand uncertainty, system contingencies, and market power, and an iterative procedure for solving this EPEC through repeated application of an MPEC algorithm is introduced. Expand
Limiting behavior of the affine scaling continuous trajectories for linear programming problems
TLDR
This work considers the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form and shows that these trajectories tend to an optimal solution which in general depends on the starting point. Expand
A geometric view of parametric linear programming
TLDR
If a polynomial-time LP solver is used to implement this subroutine, a substantial improvement on the complexity of those parametric RHS LP instances which exhibit degeneracy is obtained. Expand
Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm
TLDR
This paper describes data structures and programming techniques used in an implementation of Karmarkar's algorithm for linear programming, which relies on a direct factorization scheme, with an extensive symbolic factorization step performed in a preparatory stage of the linear programming algorithm. Expand
Two-settlement electricity markets with price caps and Cournot generation firms
TLDR
A forward cap increases firms’ incentives for forward contracting, whereas a spot cap reduces such incentives, and in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified. Expand
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