The solution of an optimal power ow (OPF) problem in rectangular form by an interior-point method (IPM) for nonlinear programming is described. When formulated in rectangular form, some OPF variants have quadratic objective and quadratic constraints. Such quadratic features allow for ease of matrix setup and inexpensive incorporation of higher-order information in a predictor-corrector procedur...

It is well known that the so-called first-order predictor-corrector methods working in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. However, the best known iteration complexity of this type of methods is O (

A-priori individual interconnect length estimates can be used to make placement efficient and reduce delay and power consumption in a circuit. However, finding lengths of individual interconnects before their terminals have been placed can be a daunting task. In this thesis, the main characteristics that need to be considered while designing an individual a-priori length estimation technique fo...

Two predictor-corrector methods of order m = Ω(logn) are proposed for solving sufficient linear complementarity problems. The methods produce a sequence of iterates in the N− ∞ neighborhood of the central path. The first method requires an explicit upper bound κ of the handicap of the problem while the second method does not. Both methods have O((1 + κ)1+1/m √ nL) iteration complexity. They are...

A nonoverlapping domain decomposition method for some time-dependent convection-diffusion equations is presented. It combines predictor-corrector technique, modified upwind differences with explicit/implicit coupling to provide intrinsic parallelism, and unconditional stability while improving the accuracy. Both rigorous mathematical analysis and numerical experiments are carried out to illustr...

The paper extends prior work by the authors on LOQO, an interior point algorithm for nonconvex nonlinear programming. The specific topics covered include primal versus dual orderings and higher order methods, which attempt to use each factorization of the Hessian matrix more than once to improve computational efficiency. Results show that unlike linear and convex quadratic programming, higher o...

We discuss a procedure for numerically approximating solutions to a system of nonlinear partial diierential equations which describe mountain pine beetles attacking lodgepole pine en masse. A centered spatial dicretization which yields a system of ordinary diierential equations is presented, including a method for generating`trans-parent' spatial boundary conditions. A ux-based model estimates ...

It has been shown in various papers that most interior-point algorithms and their analysis can be generalized to semidefinite optimization. This paper presents an extension of the recent variant of Mehrotra’s predictor-corrector algorithm that was proposed by Salahi et al. (2005) for linear optimization problems. Based on the NT (Nesterov and Todd 1997) direction as Newton search direction it i...

This article provides an analysis for the delay fractional differential equations in Caputo sense by an introduction of an improved predictorcorrector formula. The delay term is expressed either as a constant or time varying. The implication of this new approach is used to improvise the algorithm. A vivid description of the convergence and detailed error analysis of the improved predictor-corre...