We develop subgradientand gradient-based methods for minimizing strongly convex functions under a notion which generalizes the standard Euclidean strong convexity. We propose a unifying framework for subgradient methods which yields two kinds of methods, namely, the Proximal Gradient Method (PGM) and the Conditional Gradient Method (CGM), unifying several existing methods. The unifying framewor...

In this paper we present a variant of the proximal forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The proposed iteration, which will be call the Proximal Subgradient Splitting Method, extends the classical projected subgradient iteration for important classes of pr...

Various iterative methods are available for the approximate solution of nonsmooth minimization problems. For a popular nonsmooth minimization problem arising in image processing the suitable application of three prototypical methods and their stability is discussed. The methods are compared experimentally with a focus on choice of stopping criteria, influence of rough initial data, step sizes a...

A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due to its large scale, secondorder methods cannot solve the free material design problem in reasonable size. We formulate the free material optimization (FMO) problem into a saddle-point form in which the inverse of the ...

We consider the problem of !nding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of !nding the fastest converging linear iteration can be cast as a semide!nite program, and therefore e"ciently and globally solved. These op...

Abstract We introduce a new subgradient extragradient algorithm utilizing the concept of set solutions split modified system variational inequality problems (SMSVIP). Our main theorem is weak convergence for such an approximating fixed point problem in real Hilbert space. also apply these results to approximate minimization problem. In last section, we provide example illustrate potential our t...

A major issue in Lagrangian relaxation for integer programming problems is to maximize the dual function which is piece-wise linear, and consists of many facets. Available methods include the subgradient method, the bundle method, and the recently developed surrogate subgradient method. Each of the above methods, however, has its own limitations. Based on the insights obtained from these method...