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

An Active-Set Strategy in Interior Point Method for Linear Programming

Slacks-based measure (SBM) (Tone [1]), Pastor et al. [2]) has been widely utilized as a representative non-radial DEA model. However, this model, called SBM-Min here, evaluates the efficiency of an inefficient DMU referring to the furthest frontier point within a range. In contrast, the SBM-Max model looks for the nearest frontier point and hence its score is generally greater than the SBM-Min score. The Super-SBM model (Tone [3]) evaluates the efficiency of an efficient DMU referring to the nearest point on the frontier except itself. We can foresee a close connection between SBM-Max and Super-SBM models, because the motivations behind the two models are same. In this paper we demonstrate this consistency using a real dataset.

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On the Consistency of Slacks-based Measure-max Model and Super-slacks-based Measure Model

The network dea model

Editorial: Network-DEA in the service sector

It has been pointed out that DEA scores may be influenced by several external environmental factors, which are uncontrollable for DMUs. It implies that the DEA efficiency score without data adjustment might be biased and impractical for measuring genuine management efficiency. Therefore it is essential to eliminate uncontrollable effects from DEA scores and evaluate “pure” managerial efficiency for DMUs. In an effort to solve this problem, we employ a multi-stage data adjustment procedure using DEA and regression models, which is originally proposed by Fried et al. [1999] consisting of four stages. In this study, we further modify this procedure by introducing newly developed devices in each stage; Connected Slacks-Based Measure (CSBM) model at the first and fourth stages, the Tobit model with DMU dummies at the second stage, and a data tuning procedure at the third stage. Then we decompose the technical inefficiency into three factors, i.e. environmental effects, time shift effects and pure technical inefficiency. Lastly, we apply this procedure to the electric power utilities in Japan and the US and compare their pure technical efficiency and causes of inefficiency.

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Kaoru Tone

Papers

An Active-Set Strategy in Interior Point Method for Linear Programming

On the Consistency of Slacks-based Measure-max Model and Super-slacks-based Measure Model

The network dea model

Editorial: Network-DEA in the service sector

2-B-5 Separation of uncontrollable factors and time shift effects from DEA scores