We propose methods for robust discrete optimization in which the objective function has cost components that are subject to independent and bounded perturbations. Motivated by risk management practice, we approximate the problem of optimization of VaR, a widely used downside risk measure by introducing four approximating models that origininate in robust optimization. We show that all four mode...

Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the ge...

There is renewed interest in the development of effective and efficient methods for optimizing models of which the optimizer has no structural knowledge. This is what in the literature is referred to as optimization of black boxes. In particular, we address the challenge of optimizing expensive black boxes, that is, those that require a significant computational effort to be evaluated. We descr...

We study statistical inference and robust solution methods for stochastic optimization prob-lems. We first develop an empirical likelihood framework for stochastic optimization. We showan empirical likelihood theory for Hadamard differentiable functionals with general f -divergencesand give conditions under which T (P ) = infx∈X EP [`(x; ξ)] is Hadamard differentiable. Noting<lb...

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter λ ∈ R, so-called parametric...

We consider robust optimization for polynomial optimization problems where the uncertainty set is a set of candidate probability density functions. This set is a ball around a density function estimated from data samples, i.e., it is data-driven and random. Polynomial optimization problems are inherently hard due to nonconvex objectives and constraints. However, we show that by employing polyno...

Smart field technology is an attractive research field, as it can find an optimal well control strategy to maximize the oil recovery or the net present value (NPV). As the subsurface geology is highly uncertain, the reservoir model is usually described by a set of reservoir models. In well control optimization for a reservoir described by a set of geological models, the expectation of NPV is op...

in this paper a new strategy is proposed to design a fixed-structure robust controller for a flexible beam.  robust controller designed by the conventional  loop­ shaping method is not appropriate for a beam because of its high order and complicated form. fixed-structure  loop shaping control in conjunction with particle swarm optimization (pso)algorithm  is used to overcome this drawback. the ...

Modern compilers present a large number of optimization options covering the many alternatives to achieving high performance for different kinds of applications and workloads. Selecting the optimal set of optimization options for a given application and workload becomes a real issue since optimization options do not necessarily improve performance when combined with other options. The ESTO fram...