A decomposition procedure based on approximate newton directions

The efficient solution of large-scale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decomposed subproblems. We also study how to correct these directions using (decomposable) preconditioned conjugate gradient methods to ensure local convergence in all cases. The choice of appropriate preconditioners results in a natural manner from the structure in the problem. Finally, we conduct computational experiments to compare the resulting procedures with direct methods, as well as to study the impact of different preconditioner choices

A DECOMPOSITION PROCEDURE BASED ON APPROXIMATE NEWTON DIRECTIONS

The efficient solution of large-scale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decomposed subproblems. We also study how to correct these directions using (decomposable) preconditioned conjugate gradient methods to ensure local convergence in all cases. The choice of appropriate preconditioners results in a natural manner from the structure in the problem. Finally, we conduct computational experiments to compare the resulting procedures with direct methods, as well as to study the impact of different preconditioner choices.

A decomposition procedure based on approximate Newton directions

The original publication is available at www.springerlink.comThe efficient solution of large-scale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decomposed subproblems. We also study how to correct these directions using (decomposable) preconditioned conjugate gradient methods to ensure local convergence in all cases. The choice of appropriate preconditioners results in a natural manner from the structure in the problem. Finally, we conduct computational experiments to compare the resulting procedures with direct methods.Publicad

A decomposition procedure based on approximate Newton directions.

Abstract. The efficient solution of large-scale linear and nonlinear optimization problems may require exploiting any special structure in them in an efficient manner. We describe and analyze some cases in which this special structure can be used with very little cost to obtain search directions from decomposed subproblems. We also study how to correct these directions using (decomposable) preconditioned conjugate gradient methods to ensure local convergence in all cases. The choice of appropriate preconditioners results in a natural manner from the structure in the problem. Finally, we conduct computational experiments to compare the resulting procedures with direct methods

Short-term scheduling in multi-stage batch plants through Lagrangean decomposition.

In this work, a continuous-time Mixed-Integer Linear Programming (MILP) model for the short-term scheduling in multi-stage batch plants is used. The MILP model accounts for ready unit times, release order times, sequence-dependent changeovers, transfer times between adjacent processing stages and different intermediates storage policies. A Lagrangean decomposition technique (Conejo et al., 2002) is applied to the MILP model in order to facilitate the resolution of real-world industrial cases. The proposed decomposition technique is thoroughly examined. An industrial case study of a multi-product multi-stage pharmaceuticals batch plant is addressed in order to demonstrate the performance and the advantages of the proposed decomposition scheme. The pharmaceutical plant under study consists of 17 processing equipments. The numerous (30 to 50) final products require 5 to 6 processing stages. Sequence-dependent changeovers are permitted in most stages. It is noteworthy that changeovers are usually of the same order of magnitude or even larger than the processing times. The main optimization goal is the minimization of the makespan. Results obtained are discussed highlighting the advantages and the special characteristics of the proposed scheduling model.Peer ReviewedPostprint (published version

A Response-Function-Based Coordination Method for Transmission-Distribution-Coupled AC OPF

With distributed generation highly integrated into the grid, the transmission-distribution-coupled AC OPF (TDOPF) becomes increasingly important. This paper proposes a response-function-based coordination method to solve the TDOPF. Different from typical decomposition methods, this method employs approximate response functions of the power injections with respect to the bus voltage magnitude in the transmission-distribution (T-D) interface to reflect the "reaction" of the distribution to the transmission system control. By using the response functions, only one or two iterations between the transmission system operator (TSO) and the distribution system operator(s) (DSO(s)) are required to attain a nearly optimal TDOPF solution. Numerical tests confirm that, relative to a typical decomposition method, the proposed method does not only enjoy a cheaper computational cost but is workable even when the objectives of the TSO and the DSO(s) are in distinct scales.Comment: This paper will appear at 2018 IEEE PES Transmission and Distribution Conference and Expositio

Solving dynamic stochastic economic models by mathematical programming decomposition methods.

Discrete-time optimal control problems arise naturally in many economic problems. Despite the rapid growth in computing power and new developments in the literature, many economic problems are still quite challenging to solve. Economists are aware of the limitations of some of these approaches for solving these problems due to memory and computational requirements. However, many of the economic models present some special structure that can be exploited in an efficient manner. This paper introduces a decomposition methodology, based on a mathematical programming framework, to compute the equilibrium path in dynamic models by breaking the problem into a set of smaller independent subproblems. We study the performance of the method solving a set of dynamic stochastic economic models. The numerical results reveal that the proposed methodology is efficient in terms of computing time and accuracyDynamic stochastic economic model; Computation of equilibrium; Mathematical programming; Decomposition techniques;