Convex optimization

About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.

Kullback-Leibler divergence constrained distributionally robust optimization

Abstract: In this paper we study distributionally robust optimization (DRO) problems where the ambiguity set of the probability distribution is defined by the Kullback-Leibler (KL) divergence. We consider DRO problems where the ambiguity is in the objective function, which takes a form of an expectation, and show that the resulted minimax DRO problems can be formulated as a one-layer convex minimization problem. We also consider DRO problems where the ambiguity is in the constraint. We show that ambiguous expectation-constrained programs may be reformulated as a one-layer convex optimization problem that takes the form of the Benstein approximation of Nemirovski and Shapiro (2006). We further consider distributionally robust probabilistic programs. We show that the optimal solution of a probability minimization problem is also optimal for the distributionally robust version of the same problem, and also show that the ambiguous chance-constrained programs (CCPs) may be reformulated as the original CCP with an adjusted confidence level. A number of examples and special cases are also discussed in the paper to show that the reformulated problems may take simple forms that can be solved easily. The main contribution of the paper is to show that the KL divergence constrained DRO problems are often of the same complexity as their original stochastic programming problems and, thus, KL divergence appears a good candidate in modeling distribution ambiguities in mathematical programming.

Compressed channel sensing

Abstract: Reliable wireless communications often requires accurate knowledge of the underlying multipath channel. This typically involves probing of the channel with a known training waveform and linear processing of the input probe and channel output to estimate the impulse response. Many real-world channels of practical interest tend to exhibit impulse responses characterized by a relatively small number of nonzero channel coefficients. Conventional linear channel estimation strategies, such as the least squares, are ill-suited to fully exploiting the inherent low-dimensionality of these sparse channels. In contrast, this paper proposes sparse channel estimation methods based on convex/linear programming. Quantitative error bounds for the proposed schemes are derived by adapting recent advances from the theory of compressed sensing. The bounds come within a logarithmic factor of the performance of an ideal channel estimator and reveal significant advantages of the proposed methods over the conventional channel estimation schemes.

Similarity Metric Learning for Face Recognition

Abstract: Recently, there is a considerable amount of efforts devoted to the problem of unconstrained face verification, where the task is to predict whether pairs of images are from the same person or not. This problem is challenging and difficult due to the large variations in face images. In this paper, we develop a novel regularization framework to learn similarity metrics for unconstrained face verification. We formulate its objective function by incorporating the robustness to the large intra-personal variations and the discriminative power of novel similarity metrics. In addition, our formulation is a convex optimization problem which guarantees the existence of its global solution. Experiments show that our proposed method achieves the state-of-the-art results on the challenging Labeled Faces in the Wild (LFW) database [10].

Fault Detection for T-S Fuzzy Time-Delay Systems: Delta Operator and Input-Output Methods

Abstract: This paper focuses on the problem of fault detection for Takagi–Sugeno fuzzy systems with time-varying delays via delta operator approach. By designing a filter to generate a residual signal, the fault detection problem addressed in this paper can be converted into a filtering problem. The time-varying delay is approximated by the two-term approximation method. Fuzzy augmented fault detection system is constructed in $\delta $ -domain, and a threshold function is given. By applying the scaled small gain theorem and choosing a Lyapunov–Krasovskii functional in $\delta $ -domain, a sufficient condition of asymptotic stability with a prescribed $H_\infty $ disturbance attenuation level is derived for the proposed fault detection system. Then, a solvability condition for the designed fault detection filter is established, with which the desired filter can be obtained by solving a convex optimization problem. Finally, an example is given to demonstrate the feasibility and effectiveness of the proposed method.