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).

/pdf/snopt-an-sqp-algorithm-for-large-scale-constrained-tznz7lt9u8.pdf

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)

/pdf/what-determines-productivity-2hh0dpac5x.pdf

What Determines Productivity

On feature selection, as one of the critical steps to develop a distress prediction model (DPM), a variety of expert systems and machine learning approaches have analytically supported developers. Data envelopment analysis (DEA) has provided this support by estimating the novel feature of managerial efficiency, which has frequently been used in recent two-stage DPMs. As key contributions, this study extends the application of expert system in credit scoring and distress prediction through applying diverse DEA models to compute corporate market efficiency in addition to the prevailing managerial efficiency, and to estimate the decomposed measure of mix efficiency and investigate its contribution compared to Pure Technical Efficiency and Scale Efficiency in the performance of DPMs. Further, this paper provides a comprehensive comparison between two-stage DPMs through estimating a variety of DEA efficiency measures in the first stage and employing static and dynamic classifiers in the second stage. Based on experimental results, guidelines are provided to help practitioners develop two-stage DPMs; to be more specific, guidelines are provided to assist with the choice of the proper DEA models to use in the first stage, and the choice of the best corporate efficiency measures and classifiers to use in the second stage.

A comparative analysis of two-stage distress prediction models

In this paper, we will discuss subjects related to virtual multipliers in the cone-ratio model in DEA. Usually, there exists ambiguity in the virtual multipliers in the polyhedral cone-ratio method when some exemplary efficient DMUs’ multipliers are employed as the admissible directions of the cone. We will propose three practical methods for resolving this ambiguity, along with an example. Then, we will discuss possible applications of vertex enumeration software, based on the Double Description Method.

Several Algorithms to Determine Multipliers for Use in Cone-Ratio Envelopment Approaches to Efficiency Evaluations in DEA

It has been well recognized that to thoroughly evaluate a firm’s performance, the evaluator must assess not only its past and present records but also future potential. However, to the best of our knowledge, there are no data envelopment analysis (DEA)-type models proposed in the literature that simultaneously take past, present and, especially, future performance indicators into account. Hence, this research aims at developing a new type of DEA model referred to as Intertemporal DEA models that can be used to fully measure a firm’s efficiency by explicitly considering its key inputs and outputs involving the past-present-future time span. In this research, the proposed Intertemporal DEA models are applied to the performance evaluation of high-tech Integrated Circuit design companies in Taiwan to demonstrate their advantages over other DEA models that ignore intertemporal efficiency.

https://papers.ssrn.com/sol3/Delivery.cfm/jors_2013_139.pdf?abstractid=2534374&mirid=1

Kaoru Tone

Papers

A comparative analysis of two-stage distress prediction models

Several Algorithms to Determine Multipliers for Use in Cone-Ratio Envelopment Approaches to Efficiency Evaluations in DEA

Past-present-future Intertemporal DEA models

A comparative study on AHP and DEA

Cost Efficiency and Returns to Scale in Life Insurance Corporation of India Using Data Envelopment Analysis