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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)
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)
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)
Design for Reliability of Low-voltage, Analog, switched-capacitor circuits play a critical role in mixed-signal, analog-to-digital interfaces. They implement a large class of functions, such as sampling , filtering, and digitization. Furthermore, their implementation makes them suitable for integration with complex, digital-signal-processing blocks in a(More)
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)
We present a new definition of optimality intervals for the parametric right-hand side linear programming (parametric RHS LP) Problem ϑ(λ) = min{c t x¦Ax =b + λ¯b,x ≥ 0}. We then show that an optimality interval consists either of a breakpoint or the open interval between two consecutive breakpoints of the continuous piecewise linear convex function ϑ(λ).(More)
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)
— 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)
In 1951, Dantzig showed the equivalence of linear programming problems and two-person zero-sum games. However, in the description of his reduction from linear programs to zero-sum games, he noted that there was one case in which the reduction does not work. This also led to incomplete proofs of the relationship between the Minimax Theorem of game theory and(More)