This paper is mainly devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from both viewpoints of optimization theory and its applications. Based on second- order generalized differential tools of variational analysis, we obtain … Read more
This paper provides an overview of developments in robust optimization and robustness published in the academic literature over the past five years. CitationTechnical report, LAMSADE, Universite Paris-Dauphine, Paris, France. (2012)ArticleDownload View PDF
This paper describes a multi-range robust optimization approach applied to the problem of capacity investment under uncertainty. In multi-range robust optimization, an uncertain parameter is allowed to take values from more than one uncertainty range. We consider a number of possible projects with anticipated costs and cash flows, and an investment decision to be made … Read more
We develop the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. A robust decision-making framework is built on a utility set which characterizes a decision maker’s risk attitude described by boundary and auxiliary conditions. This framework is studied using the Sample Average Approximation (SAA) approach. We show the … Read more
In 2001, info-gap decision theory re-invented the then 40-year old model of local robustness, known universally as radius of stability (circa 1960). Since then, this model of local robustness has been promoted by info-gap scholars as a reliable tool for the management of a severe uncertainty that is characterized by a vast (e.g. unbounded) uncertainty … Read more
In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It … Read more
This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more
Scarf’s min-max order formula for the distribution-free risk-neutral newsvendor problem is a classical result in the field of inventory management. The min-max order formula provides, in closed-form, the order quantity that maximizes the worst-case expected profit associated with the demand of a single product when only the mean and variance of the product’s demand distribution, … Read more
Eliciting the utility of a decision maker is difficult. In this paper, we develop a flexible decision making framework, which uses the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. The ideas are developed by giving a probabilistic interpretation to utility and marginal utility functions. Boundary and additional … Read more
This paper deals with the problem of determining the optimal size of a residential grid-connected photovoltaic system to meet a certain CO2 reduction target at a minimum cost. Ren et al. proposed a novel approach using a simple linear programming that minimizes the total energy costs for residential buildings in Japan. However, their approach is … Read more