Ernst Roos In this paper, we design an algorithm for maximizing a convex function over a convex feasible set. The algorithm consists of two phases: in phase 1 a feasible solution is obtained that is used as an initial starting point in phase 2. In the latter, a biconvex problem equivalent to the original problem is solved … Read more
Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more
Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is commonly used in practice as it requires specification of only a few characteristics of the activities’ duration. Moreover, its computational burden is extremely low. Over the years, four main disadvantages of PERT have … Read more
In many optimization problems uncertain parameters appear in a convex way, which is problematic as common techniques can only handle concave uncertainty. In this paper, we provide a systematic way to construct conservative approximations to such problems. Specifically, we reformulate the original problem as an adjustable robust optimization problem in which the nonlinearity of the … Read more
Although Robust Optimization is a powerful technique in dealing with uncertainty in optimization, its solutions can be too conservative when it leads to an objective value much worse than the nominal solution or even to infeasibility of the robust problem. In practice, this can lead to robust solutions being disregarded in favor of the nominal … Read more
In this paper we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem … Read more