It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of...

We present a framework for inverse optimization in a Markowitz portfolio model that is extended to include a third criterion. The third criterion causes the traditional nondominated frontier to become a surface. Until recently, it had not been possible to compute such a surface. But by using a...

A systematic approach to estimate parameters from noisy priors is proposed for traffic assignment problems. It extends inverse optimization theory to nonlinear problems, and defines a new class of parameter estimation problems in the transportation literature for networks under congestion. The...

A parameter estimation method is proposed for calibrating the household activity pattern problem so that it can be used as a disaggregate, activity-based analog of the traffic assignment problem for activity-based travel forecasting. Inverse optimization is proposed for estimating parameters of...

We consider an inverse quadratic programming (QP) problem in which the parameters in both the objective function and the constraint set of a given QP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a linear...

The inverse p-median problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices becomes a p-median with respect to the new edge lengths. The problem is shown to be strongly <InlineEquation ID="IEq1">...</inlineequation>

The focus of this paper is on studying an inverse second-order cone quadratic programming problem, in which the parameters in the objective function need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization...

We propose a parameter estimation method based on what we call the minimum decisional regret principle. We focus on mathematical programming models with objective functions that depend linearly on costs or other parameters. The approach is illustrated for cost estimation in production planning...

This paper proposes a systematic approach to certain parameter estimation problems relevant to applied optimization models. A context-specific measure of decision maker performance called decisional efficiency is defined as a function of the unknown parameter vector. The values of this measure...

We consider a manufacturer who uses a reverse, or procurement, auction to determine which supplier will be awarded a contract. Each bid consists of a price and a set of nonprice attributes (e.g., quality, lead time). The manufacturer is assumed to know the parametric form of the suppliers' cost...