A new signal processing framework based on the projections onto convex sets (POCS) is developed for solving convex optimization problems. The dimension of the minimization problem is lifted by one and the convex sets corresponding to the epigraph of the cost function are defined. If the cost function is a convex function in RN the corresponding epigraph set is also a convex set in RN+1. The ite...

A new signal processing framework based on the projections onto convex sets (POCS) is developed for solving convex optimization problems. The dimension of the minimization problem is lifted by one and the convex sets corresponding to the epigraph of the cost function are defined. If the cost function is a convex function in RN the corresponding epigraph set is also a convex set in RN+1. The ite...

This paper deals with convex optimization problems in the face of data uncertainty within the framework of robust optimization. It provides various properties and characterizations of the set of all robust optimal solutions of the problems. In particular, it provides generalizations of the constant subdifferential property as well as the constant Lagrangian property for solution sets of convex ...

This paper is devoted to constructing a definite efficient scheme for non-smooth optimization. A separating plane algorithm with additional clipping is proposed. The algorithm is used for solving the unconstrained non-smooth convex optimization problem. The latter problem can be reformulated as the computation of the value of a conjugate function at the origin. The algorithm convergence is prov...

Abstract We consider the convex quadratic optimization problem in $$\mathbb {R}^{n}$$ R n with indicator variables and arbitrary constraints on indicators. show that a hull description of associated mixed-integer set an extended space number addit...

Embedding feature selection in nonlinear SVMs leads to a challenging non-convex minimization problem, which can be prone to suboptimal solutions. This paper develops an effective algorithm to directly solve the embedded feature selection primal problem. We use a trust-region method, which is better suited for non-convex optimization compared to line-search methods, and guarantees convergence to...

Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in R the corresponding set is also a convex set in R. The iterative optimization approach start...

In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods....