A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints have to be approximated by finite expressions to generate a computable problem. Here, using the example of the topology optimization of a truss, a method is pro...

This paper presents mathematical programming techniques for solving a class of multi-sensor scheduling problems. Robust optimization problems are formulated for both deterministic and stochastic cases using linear 0–1 programming techniques. Equivalent formulations are developed in terms of cardinality constraints. We conducted numerical case studies and analyzed the performance of optimization...

We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality properties as providing suboptimality or infeasibility certificates. Our focus is on the exciting developments occurred in the last few years, including robust optimization, combinatorial optimizatio...

Our goal in this talk is to present unifying concepts for both stochastic and robust optimization problems involving infinite uncertainty sets. We apply methods from vector optimization in general spaces, set-valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming. These methods provide new in...

Simulation-optimization aims to identify the setting of the input parameters (input variables, factors) of the simulated system that leads to the optimal system performance. In practice, however, some of these parameters cannot be perfectly controlled — due to measurement errors or other implementation issues, and the inherent uncertainty caused by fluctuations in the environment (e.g., demand)...

The multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality. Working within the design space is not considered as a change. Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process. Design space is propo...

and Applied Analysis 3 independently by El-Ghaoui et al. 8, 9 propose to solve the following robust optimization problem

We denote, for all feasible x, by R(x) the associated robust problem when x is fixed, and we denote by R(x, d) the associated robust problem when x and d are fixed. In this note we assume that the deterministic problem doesn’t satisfied the full recourse property. We prove how to obtain a new MILP denoted (P̃ ) such that the robust associated problem has the same optimal solution as the initial ...

We show that a rst order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this rst order problem.