Based on the recent approach of Bertsimas and Sim \cite{bs1, bs2} to robust optimization in the presence of data uncertainty, we prove a bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. A … Read more
This paper considers robust optimization to cope with uncertainty about the stock return process in one period portfolio selection problems involving options. The ro- bust approach relates portfolio choice to uncertainty, making more cautious portfolios when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlyings and show that … Read more
Given a real function on a Euclidean space, we consider its “robust regularization”: the value of this new function at any given point is the maximum value of the original function in a fixed neighbourhood of the point in question. This construction allows us to impose constraints in an optimization problem *robustly*, safeguarding a constraint … Read more
The purpose of this note is to present a robust counterpart of the Huber estimation problem in the sense of Ben-Tal and Nemirovski when the data elements are subject to ellipsoidal uncertainty. The robust counterparts are polynomially solvable second-order cone programs with the strong duality property. We illustrate the effectiveness of the robust counterpart approach … Read more
Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible … Read more
Motivated by telecommunication applications, we investigate the shortest path problem on directed acyclic graphs under arc length uncertainties represented as interval numbers. Using a minimax-regret criterion we define and identify robust paths via mixed-integer programming and exploiting interesting structural properties of the problem. Citation Bilkent University, Department of Industrial Engineering, Technical Report August 2001 Article … Read more
Adaptive Simulated Annealing (ASA) is a C-language code developed to statistically find the best global fit of a nonlinear constrained non-convex cost-function over a D-dimensional space. Citation %A L. Ingber %R Global optimization C-code %I Caltech Alumni Association %C Pasadena, CA %T Adaptive Simulated Annealing (ASA) %D 1993 %K 200701 %L Ingber:1993:CODE-ASA %O URL http://www.ingber.com/#ASA-CODE … Read more
Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to … Read more
For a set of financial securities specified by their expected returns and variance/covariances we propose the concept of minimum risk arbitrage, characterize conditions under which such opportunities may exist. We use conic duality and convex analysis to derive these characterizations. For practical computation a decidability result on the existence of an arbitrage opportunity is derived. … Read more