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- Renato D. C. Monteiro, Ilan Adler
- Math. Program.
- 1989

We describe a primal-dual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier… (More)

- Renato D. C. Monteiro, Ilan Adler
- Math. Program.
- 1989

We describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of O(~/nL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the… (More)

- Renato D. C. Monteiro, Ilan Adler, Mauricio G. C. Resende
- Math. Oper. Res.
- 1990

We describe an algorithm for linear and convex quadratic programming problems that uses power series approximation of the weighted barrier path that passes throi^ the current iterate in order to find the next iterate. If r » 1 is the order of approximation used, we show that our algorithm has time complexity O(n'"""^'^*i."*'^'') iterations and O{n^ + n^r)… (More)

- Ilan Adler, Narendra Karmarkar, Mauricio G. C. Resende, Geraldo Veiga
- INFORMS Journal on Computing
- 1989

- Ilan Adler, Renato D. C. Monteiro
- Algorithmica
- 1992

- Jian Yao, Ilan Adler, Shmuel S. Oren
- Operations Research
- 2008

A model of two-settlement electricity markets is introduced, which accounts for flow congestion, demand uncertainty, system contingencies, and market power. We formulate the subgame perfect Nash equilibrium for this model as an equilibrium problem with equilibrium constraints (EPEC), in which each firm solves a mathematical program with equilibrium… (More)

- Jian Yao, Shmuel S. Oren, Ilan Adler
- HICSS
- 2004

— We formulate a two-settlement equilibrium in competitive electricity markets as a subgame-perfect Nash equilibrium in which each generation firm solves a Mathematical Program with Equilibrium Constraints (MPEC), given other firms' forward and spot strategies. We implement two computational approaches, one of which is based on a Penalty Interior Point… (More)

- Ilan Adler, Renato D. C. Monteiro
- Math. Program.
- 1991

We consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form. By characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems, we show that these trajectories tend to an optimal solution which in general… (More)

- Ilan Adler, Mauricio G. C. Resende, Geraldo Veiga, Narendra Karmarkar
- Math. Program.
- 1989

This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. 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. Linear programs are expressed in an inequality… (More)

- Jian Yao, Shmuel S. Oren, Ilan Adler
- European Journal of Operational Research
- 2007

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a performance-based… (More)