We show in the present paper that many open and challenging problems in control theory belong to the class of concave minimization programs. More precisely, these problems can be recast as the minimization of a concave objective function over convex LMI (Linear Matrix Inequality) constraints. In this setting, these problems can then be eeciently handled using local and/or global optimization te...

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...

A disjunctive programming problem corresponds to the minimization of an objective function on a constraint set which is a union of sets, for example, min f (x) s.t. min j∈ J g j (x) ≤ 0 where the functions f and g j are real valued defined on a Banach space X and J is a (possibly infinite) index set. This class of problems has been introduced by Balas [4] in 1974 and then studied by many author...

This paper shows that we can classify latent outliers efficiently through the process of minimizing the sum of infeasibilities (SOI). The SOI minimization has been developed in the area of convex optimization to find an initial solution, solve a feasibility problem, or check out some inconsistent constraints. It was also adopted recently as an approximation method to minimize a robust error fun...

It is well known that the gradient-projection algorithm GPA is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrain...

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem’s domain X the sum of a linear form and a strongly convex function. To make such an algorithm practical, X should be proximal-friendly – admit a strongly convex function with e...

This paper presents a decomposition method for solving convex minimization problems. At each iteration, the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables. We derive this algorithm from Rockafellar's proximal method of multipliers, which involves an augmented Lagrangian with an additional quadratic proximal term. The algorithm preserves...