The global convergence of ADMM for convex problems was given by He and Yuan in [5] under the variation inequality framework. However, since our optimization problem is non-convex, the convergence analysis for ADMM needs additional conditions. In non-convex optimization, convergence to a stationary point (local minimum) is the best convergence property that we can hope for. By imposing some cond...

This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formula...

A convex non-convex variational model is proposed for multiphase image segmen-tation. We consider a specially designed non-convex regularization term which adapts spatially tothe image structures for better controlling of the segmentation and easy handling of the intensityinhomogeneities. The nonlinear optimization problem is efficiently solved by an Alternating Direc-tions Meth...

The quality of underwater images is an important problem for resource detection. However, the light scattering and plankton in water can impact images. In this paper, a novel image restoration based on non-convex, non-smooth variation thermal exchange optimization proposed. Firstly, dark channel prior used to estimate rough transmission map. Secondly, map refined by proposed adaptive non-convex...

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms and functions. Further, iteratively propagating from node to node along edge, we prove that “regarding the neural graph without triangles, it is nearly convex ...

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. Numerical examples are illustrated. Comparing...