Ka Fai Cedric Yiu

Brief paper: Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.

Fabric defect detection using morphological filters

In this paper, a novel defect detection scheme based on morphological filters is proposed to tackle the problem of automated defect detection for woven fabrics. In the proposed scheme, important texture features of the textile fabric are extracted using a pre-trained Gabor wavelet network. These texture features are then used to facilitate the construction of structuring elements in subsequent morphological processing to remove the fabric background and isolate the defects. Since the proposed defect detection scheme requires a few morphological filters only, the amount of computational load involved is not significant. The performance of the proposed scheme is evaluated by using a wide variety of homogeneous textile images with different types of common fabric defects. The test results obtained exhibit accurate defect detection with low false alarms, thus showing the effectiveness and robustness of the proposed detection scheme. In addition, the proposed detection scheme is further evaluated in real time by using a prototyped automated inspection system.

Optimal portfolios under a value-at-risk constraint

Abstract This paper looks at the optimal portfolio problem when a value-at-risk constraint is imposed. This provides a way to control risks in the optimal portfolio and to fulfil the requirement of regulators on market risks. The value-at-risk constraint is derived for n risky assets plus a risk-free asset and is imposed continuously over time. The problem is formulated as a constrained utility maximization problem over a period of time. The dynamic programming technique is applied to derive the Hamilton–Jacobi–Bellman equation and the method of Lagrange multiplier is used to tackle the constraint. A numerical method is proposed to solve the HJB-equation and hence the optimal constrained portfolio allocation. Under this formulation, we find that investments in risky assets are optimally reduced by the imposed value-at-risk constraint.

A Hybrid Descent Method for Global Optimization

In this paper, a hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, is proposed. The simulated annealing algorithm is used to locate descent points for previously converged local minima. The combined method has the descent property and the convergence is monotonic. To demonstrate the effectiveness of the proposed hybrid descent method, several multi-dimensional non-convex optimization problems are solved. Numerical examples show that global minimum can be sought via this hybrid descent method.

Near-field broadband beamformer design via multidimensional semi-infinite-linear programming techniques

Broadband microphone arrays has important applications such as hands-free mobile telephony, voice interface to personal computers and video conference equipment. This problem can be tackled in different ways. In this paper, a general broadband beamformer design problem is considered. The problem is posed as a Chebyshev minimax problem. Using the l/sub 1/-norm measure or the real rotation theorem, we show that it can be converted into a semi-infinite linear programming problem. A numerical scheme using a set of adaptive grids is applied. The scheme is proven to be convergent when a certain grid refinement is used. The method can be applied to the design of multidimensional digital finite-impulse response (FIR) filters with arbitrarily specified amplitude and phase.

Multicriteria design of oversampled uniform DFT filter banks

Subband adaptive filters have been proposed to avoid the drawbacks of slow convergence and high computational complexity associated with time domain adaptive filters. However, subband processing causes signal degradations due to aliasing effects and amplitude distortions. This problem is unavoidable due to further filtering operations in subbands. In this letter, the problems of aliasing effect and amplitude distortion are studied. Prototype filters which are optimized with respect to those properties are designed and their performances are compared. Moreover, the effect of the number of subbands, the oversampling factors and the length of the prototype filter are also studied. Using the multicriteria formulation, all Pareto optimums are sought via the nonlinear programming technique. We find that the prototype filter designed via the Kaiser window provides the best overall performance among the methods we studied. Also, there is a critical oversampling factor beyond which the improvement of performance is diminishing. Finally, if the length of the prototype filter increases with the number of subbands, an increase in the number of subbands will not deteriorate the performance.

Optimal portfolios with regime switching and value-at-risk constraint

We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes.

Nonlinear system modeling via knot-optimizing B-spline networks

In using the B-spline network for nonlinear system modeling, owing to a lack of suitable theoretical results, it is quite difficult to choose an appropriate set of knot points to achieve a good network structure for minimizing, say, a minimum error criterion. In this paper, a novel knot-optimizing B-spline network is proposed to approximate the general nonlinear system behavior. The knot points are considered to be independent variables in the B-spline network and are optimized together with the B-spline expansion coefficients. The simulated annealing algorithm with an appropriate search strategy is used as an optimization algorithm for the training process in order to avoid any possible local minima. Examples involving dynamic systems up to six dimensions in the input space to the network are solved by the proposed method to illustrate the effectiveness of this approach.

A hybrid descent method with genetic algorithm for microphone array placement design

In beamformer design, the microphone locations are often fixed and only the filter coefficients are varied in order to improve on the noise reduction performance. However, the positions of the microphone elements play an important role in the overall performance and should be optimized at the same time. However, this nonlinear optimization problem is non-convex and local search techniques might not yield the best result. This problem is addressed in this paper. A hybrid descent method is proposed which consists of a genetic algorithm together with a gradient-based method. The gradient-based method can help to locate the optimal solution rapidly around the start point, while the genetic algorithm is used to jump out from local minima. This hybrid method has the descent property and can help us to find the optimal placement for better beamformer design. Numerical examples are provided to demonstrate the effectiveness of the method.

Placement Design of Microphone Arrays in Near-Field Broadband Beamformers

In beamformer design, the microphone array configuration is often prescribed and the filter coefficients are varied in order to improve on the noise reduction performance. However, the positions of the microphone elements play an important role in the overall performance and should be optimized at the same time. This problem is addressed in this paper. In order to understand the performance improvement through location movements, we first look at the design with an infinite filter length, which gives the performance limit for finite filter length designs. When the filter length is finite, both the filter coefficients and the placement of the microphone array are decision variables. In both situations, the problems can be formulated as constrained optimization problems. As the filter length increases, we show that the performance converges quickly to the limit. For illustration, two numerical examples are solved. Comparing with several popular configurations, we show that the performance of the optimized configuration improves significantly.