Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variab...

This paper deals with numerical Toeplitz matrix approximation. Our approach is based on (i) a projection algorithm which converges globally but slowly; and (ii) the quasi-Newton method which is faster. Hybrid methods that attempt to combine the best features of both methods are then considered.

Joint decisions in production allocation and ordering policies for single and multiple products in a production-distribution network system consisting of multiple plants are discussed, production capacity constraints of multi-plants and unit production capacity for producing a product are considered. Based on the average total cost in unit time, the decisive model is established. It tries to de...

This paper presents a new Discriminative Random Fields (DRFs) framework. Based on the DRFs framework proposed by Kumar and Hebert, the following improvements have been conducted. Firstly, the interaction potential and the associated potential model are simplified. Secondly, we reduce the dimension of the multi-scale features, re-definedimension of the single-scale feature, and increase the colo...

We consider the optimal design of a machine frame under several stress constraints. The shape optimization is based on a Quasi-Newton Method. We need to solve the plain stress state equations in a complex domain for each evaluation of the objective therein. The complexity and robustness of the optimization depends strongly on the solver for the pde. Therefore, solving the direct problem require...

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. In this paper, we describe a new efficient adaptive limited memory interior point bundle method for large, possible nonconvex, nonsmooth inequality constrained optimization. The method is a hybrid of the nonsmooth variable met...

We consider the bilevel optimisation approach proposed in [5] for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PD...

This paper considers a distributed network of through-the-wall imaging radars and provides a solution for accurate indoor scene reconstruction in the presence of multipath propagation. A sparsity-based method is proposed for eliminating ghost targets under imperfect knowledge of interior wall locations. Instead of aggregating and processing the observations at a central fusion station, joint sc...

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a mi...