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In engineering design, an optimized solution often turns out to be suboptimal, when errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we… (More)

We propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and incorporate constraints that need to be feasible under perturbations. The proposed method iteratively moves along descent directions for the robust problem with nonconvex constraints, and terminates at a robust local minimum.… (More)

- Dimitris Bertsimas, Omid Nohadani, Kwong Meng Teo
- 2007

In engineering design, the physical properties of a system can often only be described by numerical simulation. Optimization of such systems is usually accomplished heuristically without taking into account that there are implementation errors that lead to very suboptimal, and often, infeasible solutions. We present a robust optimization method for… (More)

Complex systems can be optimized to improve the performance with respect to desired functionalities. An optimized solution, however, can become suboptimal or even infeasible, when errors in implementation or input data are encountered. We report on a robust simulated annealing algorithm that does not require any knowledge of the problems structure. This is… (More)

- Dimitris Bertsimas, Omid Nohadani, Kwong Meng Teo
- 2007

In engineering design, an optimized solution often turns out to be suboptimal, when implementation errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this… (More)

- Yu Chen, Rong Yu, Weifei Li, Omid Nohadani, Stephan Haas, A F J Levi
- 2003

Using adaptive algorithms, the design of nanoscale dielectric structures for photonic applications is explored. Widths of dielectric layers in a linear array are adjusted to match target responses of optical transmission as a function of energy. Two complementary approaches are discussed. The first approach uses adaptive local random updates and… (More)

Optimized chirped mirrors may perform suboptimally, or completely fail to satisfy specifications, when manufacturing errors are encountered. We present a robust optimization method for designing these dispersion-compensating mirror systems that are used in ultrashort pulse lasers. Possible implementation errors in layer thickness are taken into account… (More)

We study field-induced magnetic order in cubic lattices of dimers with antiferromagnetic Heisenberg interactions. The thermal critical exponents at the quantum phase transition from a spin liquid to a magnetically ordered phase are determined from stochastic series expansion quantum Monte Carlo simulations. These exponents are independent of the interdimer… (More)

Intensity-Modulated Radiation Therapy (IMRT) is the technique of delivering radiation to cancer patients by using non-uniform radiation fields from select angles, with the aims of reducing the intensity of the beams that go through critical structures and reaching the dose prescription in the target volume. Two decisions are of fundamental importance: to… (More)

- Shimon Y Nof, Gary J Cheng, Andrew M Weiner, Xin W Chen, Avital Bechar, Marshall G Jones +24 others
- 2013

The purpose of this article is to review the key emerging innovations in laser and photonics systems as well as their design and integration, focusing on challenges and opportunities for solutions of societal challenges. Developments, their significance, and frontier challenges are explained in advanced manufacturing, biomedicine and healthcare, and… (More)