Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse.
We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom (say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections (about 900 examples).

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SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

Analytic hierarchy process : An overview of applications

In this paper, we will propose a Slacks-Based measure (SBM) of efficiency in DEA. This scalar measure deals directly with the input surplus and the output shortage of the decision making unit (DMU) concerned. It is unit invariant and monotone decreasing with respect to input surplus and output shortage. Furthermore, this measure is decided only by consulting with the reference set of the DMU and is not affected by statistics over the whole data set. The new measure has a close connection with other measures proposed so far, e.g., CCR and BCC. The dual side of this model can be interpreted as profit maximization, in contrast to the ratio maximization of the CCR model. Numerical experiments show its validity as an efficiency measurement tool and its compatibility with other measures of efficiency.

A Slacks Based Measure of Efficiency in Data Envelopment Analysis

A slacks-based measure of super-efficiency in data envelopment analysis

Economists have shown that large and persistent differences in productivity levels across businesses are ubiquitous. This finding has shaped research agendas in a number of fields, including (but not limited to) macroeconomics, industrial organization, labor, and trade. This paper surveys and evaluates recent empirical work addressing the question of why businesses differ in their measured productivity levels. The causes are manifold, and differ depending on the particular setting. They include elements sourced in production practices -- and therefore over which producers have some direct control, at least in theory -- as well as from producers' external operating environments. After evaluating the current state of knowledge, I lay out what I see are the major questions that research in the area should address going forward. (JEL D24, G31, L11, M10, O30, O47)

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What Determines Productivity

Measures of inefficiency in data envelopment analysis and stochastic frontier estimation

Firstly, we discuss differences between Farrell and Pareto-Koopmans efficiency measures in DEA, and propose a composite method for discriminating them. Then, we extend the method to so-called “epsilon based-measure (EBM).” The EBM can examine the robustness and stability of efficiency measure of DMUs regarding parametric change of input multiplier variables. Lastly, we propose a scheme for selecting an appropriate value of epsilon with recourse to actual cost shares of input resources.

An epsilon-based measure of efficiency in DEA

A Strange Case of the Cost and Allocative Efficiency in DEA

Decomposing capacity utilization in data envelopment analysis: An application to banks in India

We propose a dynamic DEA model involving network structure in each period within the framework of a slacks-based measure approach. We have previously published the network SBM (NSBM) and the and, horizontally, we combine the network structure by means of carry-over activities between two succeeding periods. This model can evaluate (1) the overall efficiency over the entire observed period, (2) dynamic change of period efficiency and (3) dynamic change of divisional efficiency. The model can be implemented in input-, outputor non-(both) oriented forms under the CRS or VRS assumptions on the production possibility set. Finally, we applied this model to a dataset of US electric utilities and compared the result with that of DSBM. & 2013 Elsevier Ltd. All rights reserved.

Kaoru Tone

Papers

Measures of inefficiency in data envelopment analysis and stochastic frontier estimation

An epsilon-based measure of efficiency in DEA

A Strange Case of the Cost and Allocative Efficiency in DEA

Decomposing capacity utilization in data envelopment analysis: An application to banks in India

Dynamic DEA with network structure_ A slacks-based measure approach