Most research in robust optimization has so far been focused on inequalityonly, convex conic programming with simple linear models for uncertain parameters.

Planning problems are often formulated as heuristic search. The choice of the heuristic function plays a significant role in the performance of planning systems, but a good heuristic is not always available. We propose a new approach to learning heuristic functions from previously solved problem instances in a given domain. Our approach is based on approximate linear programming, commonly used in reinforcement learning. We show that our approach can be used effectively to learn admissible heuristic estimates and provide an analysis of the accuracy of the heuristic. When applied to common heuristic search problems, this approach reliably produces good heuristic functions.

In this paper we present robust models for index tracking and active portfolio management. The goal of these models is to control the e#ect of statistical errors in estimating market parameters on the performance of the portfolio. The proposed models allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta, limits on cash exposure, etc. The optimal portfolios are computed by solving second-order cone programs. Since the complexity of solving a second-order cone program is comparable to that of solving a convex quadratic program, it follows that the e#ort required to compute the optimal robust portfolio is comparable to that of computing the Markowitz optimal portfolio. We report on the performance of our robust strategies in tracking the S&P 500 index over 1994-2003. We find that our robust strategy is able to track the index with a significantly smaller number of assets than a non-robust mean-variance index tracking strategy. We propose a simple strategy for managing the cost of the robust index tracking strategy in markets with transaction costs. Our computational results also suggest that the robust active portfolio management strategy significantly outperforms the S&P 500 index without a significant increase in volatility. 1

We consider the design of tapers for coupling power between uniform and slowlight periodic waveguides. We describe new optimization methods 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. We introduce 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. We compare our robust design results to a linear taper, and to optimized tapers that do not take parameter variation into account. Finally, we verify the robust performance of our designs using an accurate, but much more expensive, method for evaluating the reflection coefficient. Key words. Robust optimization, PDE-constrained optimization, shape optimization, coupling taper, periodic waveguide, slow-light, photonics.

Abstract—Long design cycles due to the inability to predict silicon realities are a well-known problem that plagues analog/RF integrated circuit product development. As this problem worsens for nanoscale IC technologies, the high cost of design and multiple manufacturing spins causes fewer products to have the volume required to support full-custom implementation. Design reuse and analog synthesis make analog/RF design more affordable; however, the increasing process variability and lack of modeling accuracy remain extremely challenging for nanoscale analog/RF design. We propose a regular analog/RF IC using metal-mask configurability design methodology Optimization with Recourse of Analog Circuits including Layout Extraction (ORACLE), which is a combination of reuse and shared-use by formulating the synthesis problem as an optimization with recourse problem. Using a two-stage geometric programming with recourse approach, ORACLE solves for both the globally optimal shared and application-specific variables. Furthermore, robust optimization is proposed to treat the design with variability problem, further enhancing the ORACLE methodology by providing yield bound for each configuration of regular designs. The statistical variations of the process parameters are captured by a confidence ellipsoid. We demonstrate ORACLE for regular Low Noise Amplifier designs using metal-mask configurability, where a range of applications share common underlying structure and application-specific customization is performed using the metal-mask layers. Two RF oscillator design examples are shown to achieve robust designs with guaranteed yield bound. Index Terms—Configurable design, optimization with recourse, robustness, statistical optimization. I.