Distributionally robust profit opportunities

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are considered. The infinite dimensional primal problems are formulated, leading to their simpler finite dimensional dual problems. A principal motivating question is how distributional ambiguity helps or hurts the robustness of the profit opportunity. Towards answering this question, some theory is developed and computational experiments are conducted. Finally some open questions and suggestions for future research are discussed.     

Robust canonical correlations: A comparative study

Summary  Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust) correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared with the more traditional approach to robust canonical correlation via covariance matrix estimates. A simulation study compares the performance of the different estimators under several kinds of sampling schemes. Robustness is studied as well by breakdown plots.     

Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N. The research was partially supported by BSF grant #2002038     

Sequential Semidefinite Program for Maximum Robustness Design of Structures under Load Uncertainty

A robust structural optimization scheme as well as an optimization algorithm are presented based on the robustness function. Under the uncertainties of the external forces based on the info-gap model, the maximization of the robustness function is formulated as an optimization problem with infinitely many constraints. By using the quadratic embedding technique of uncertainty and the S-procedure, we reformulate the problem into a nonlinear semidefinite programming problem. A sequential semidefinite programming method is proposed which has a global convergent property. It is shown through numerical examples that optimum designs of various linear elastic structures can be found without difficulty.The authors are grateful to the Associate Editor and two anonymous referees for handling the paper efficiently as well as for helpful comments and suggestions.     

LMI Approach to Robust Delay-Dependent Mixed H 2/H ∞ Controller of Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays

The design of a robust mixed H ₂/H _∞ controller for a class of uncertain neutral systems with discrete, distributed, and input time-varying delays is considered. More precisely, the proposed robust mixed H ₂/H _∞ controller minimizes an upper bound of the H ₂ performance measure, while guaranteeing an H _∞ norm bound constraint. Based on the Lyapunov-Krasovskii functional theory, a delay-dependent criterion is derived for the existence of a desired mixed H ₂/H _∞ controller, which can be constructed easily via feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem satisfying some LMI constraints is formulated to obtain a suboptimal robust mixed H ₂/H _∞ controller achieving the minimization of an upper bound of the closed-loop H ₂ performance measure. Finally, a numerical example is illustrated to show the usefulness of the obtained design method.The research reported here was supported by the National Science Council of Taiwan, ROC under Grant NSC 94-2213-E-507-002.     

Electrode wear-compensation of electric discharge scanning process using a robust gap-control

Robust gap-control is applied to compensate for electrode wear in an electric discharge scanning (ED-Scanning) process. This control compensates for the wear without reference to the wear ratio of the electrodes. An auxiliary gap-control loop in the vertical direction can compensate for the wear of the electrode, according to the discharge voltage when the electrode is driven along the two horizontal axes. A proportional controller for a gap-control system with maximal robustness is designed and robustly analyzed to override the non-linear and time-varying feedback. The simulated and practical responses of such a robust gap-control system yield favorable performances. The controller can maintain the location of the discharge on the vertical axis and fix the depth of the removal to that of a particular layer. The practical scanning process reveals that the dimension of a hole can be guaranteed only if the data concerning the depth of removal under specific discharge conditions and electrode diameters are applied.     

A Multi‐Strategic Concept‐Spotting Approach for Robust Understanding of Spoken Korean

We propose a multi‐strategic concept‐spotting approach for robust spoken language understanding of conversational Korean in a hostile recognition environment such as in‐car navigation and telebanking services. Our concept‐spotting method adopts a partial semantic understanding strategy within a given specific domain since the method tries to directly extract pre‐defined meaning representation slot values from spoken language inputs. In spite of partial understanding, we can efficiently acquire the necessary information to compose interesting applications because the meaning representation slots are properly designed for specific domain‐oriented understanding tasks. We also propose a multi‐strategic method based on this concept‐spotting approach such as a voting method. We present experiments conducted to verify the feasibility of these methods using a variety of spoken Korean data.     

Disturbance Attenuation in Hyperbolic 2D-systems

We consider disturbed linear 2D-systems of Fornasini–Marchesini type in the continuous time case. These systems are also named Goursat-type systems. Conditions for unique solvability of the disturbed optimal control problem with a quadratic cost functional are obtained. The disturbed or worst case optimal control guarantees to minimize the cost functional for any unknown disturbance input. In a second part then we consider a disturbance attenuation by boundary controls, i.e., by using the Goursat-data as control functions. In the 2D-case this results in two control functions acting independently on the system. We study a cooperative and a non-cooperative situation. In the cooperative situation we again obtain a disturbed optimal control problem and get conditions for existence and uniqueness of such a disturbed optimal control problem. If the action of the agents is non-cooperative we assume that it is agreed that they act on an open-loop Nash/worst-case equilibrium strategy. Sufficient conditions for the existence of such an equilibrium are obtained. Published online: April 2006     

Minimizing maximal regret in the single machine sequencing problem with maximum lateness criterion

In this paper, the single machine sequencing problem with maximum lateness criterion is discussed. The parameters of the problem are imprecise and they are specified as intervals. The maximal regret criterion is applied to calculate the optimal sequence. A polynomial algorithm for the studied problem is constructed.     

The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem.