Both sparse coding and rank minimization have led to great successes in various image processing tasks. Though the underlying principles of these two approaches are similar, no theory is available to demonstrate the correspondence. In this paper, starting by designing an adaptive dictionary for each group of image patches, we analyze the sparsity of image patches in each group using the rank mi...

Matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. However, the problem is in general NP-hard, and it is computationally hard to solve directly in practice. In this paper, we provide a new kind of approximation functions for the rank of matrix, and the corresponding approximation problems can be used to approximate ...

1 Abstract We consider the situation where the decision procedure of an interactive expert system must repeatedly solve a logic minimization problem. In that setting, the response time is slow if the instances of the logic minimization problem are diicult to solve. We propose an alternate process. It utilizes a logic problem decomposition and replaces some instances of the logic minimization pr...

Combinatorial problems arising in diverse application domains and the growing complexity of many real-world situations emphasize the need for efficient solving methods. One such problem is the bandwidth minimization problem having broad applications in engineering, science, logistics or information recovery. This well-knownNP-complete problem refers to the minimization of the bandwidth for non-...

Minimization of the L∞ norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving the problem at the heart of L∞ norm minimization are slow, and therefore cannot scale to large problems. A new method for the minimization of the L∞ norm is presente...

We consider the expected residual minimization formulation of the stochastic R0 matrix linear complementarity problem. We show that the involved matrix being a stochastic R0 matrix is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded. Moreover, local and global error bounds are given for the stochastic R0 matrix li...

We describe an application of nonlinear optimization in interferometric optical astronomy. The aim is to find the relative positions of the output pupils and the modulus of the beams through each pupil of a linear array of telescopes in order to design an instrument capable of imaging exoplanets. The problem is modelized under the form of a semi-infinite nonlinear minimization problem. The mode...

Simultaneous routing and resource allocation has been considered in wireless networks for its performance improvement. In this paper we propose a cross-layer optimization framework for worst-case queue length minimization in some type of FDMA based wireless networks, in which the the data routing and the power allocation problem are jointly optimized with Fuzzy distributed H∞ control strategy ....

Assembly lines are special kinds of production systems which are of great importance in the industrial production of high quantity commodities. In many practical manufacturing systems, configuration of assembly lines is fixed and designing a new line may be incurred huge amount of costs and thereby it is not desirable for practitioners. When some changes related to market demand occur, it is wo...

Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...