We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.

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The increasing processing capability of Multi-Processor Systemson-Chips (MPSoCs) is leading to an increase in chip power dissipation, which in turn leads to significant increase in chip temperature. An important challenge facing the MPSoC designers is to achieve the highest performance system operation that satisfies the temperature and power consumption constraints. The frequency of operation of the different processors and the application workload assignment play a critical role in determining the performance, power consumption and temperature profile of the MPSoC. In this paper, we propose novel convex optimization based methods that solve this important problem of temperature-aware processor frequency assignment, such that the total system performance is maximized and the temperature and power constraints are met. We perform experiments on several realistic SoC benchmarks using a cycle-accurate FPGA-based thermal emulation platform, which show that the systems designed using our methods meet the temperature and power consumption requirements at all time instances, while achieving maximum performance.

With technology advances, the number of cores integrated on a chip and their speed of operation is increasing. This, in turn is leading to a significant increase in chip temperature. Temperature gradients and hot-spots not only affect the performance of the system, but also lead to unreliable circuit operation and affect the life-time of the chip. Meeting the temperature constraints and reducing the hot-spots are critical for achieving reliable and efficient operation of complex multi-core systems. In this work, we present Pro-Temp, a convex optimization based method that pro-actively controls the temperature of the cores, while minimizing the power consumption and satisfying application performance constraints. The method guarantees that the temperature of the cores are below a userdefined threshold at all instances of operation, while also reducing the hot-spots. We perform experiments on several realistic multicore benchmarks, which show that the proposed method guarantees that the cores never exceed the maximum temperature limit, while matching the application performance requirements. We compare this to traditional methods, where we find several temperature violations during the operation of the system. KeywordsThermal-aware design, temperature control, dynamic frequency scaling, static and dynamic optimization.

This article concerns the design of tapers for coupling power between uniform and slow-light periodic waveguides. New optimization methods are described for designing robust tapers, which not only perform well under nominal conditions, but also over a given set of parameter variations. When the set of parameter variations models the inevitable variations typical in the manufacture or operation of the coupler, a robust design is one that will have a high yield, despite these parameter variations.The ideas of successive refinement, and robust optimization based on multi-scenario optimization with iterative sampling of uncertain parameters, using a fast method for approximately evaluating the reflection coefficient, are introduced. Robust design results are compared to a linear taper, and to optimized tapers that do not take parameter variation into account. Finally, robust performance of the resulting designs is verified using an accurate, but much more expensive, method for evaluating the reflection coefficient.