The feasibility problem for constant scaling in output feedback control is considered. This is an inherently di cult problem [20, 21] since the set of feasible solutions is nonconvex and may be disconnected. Nevertheless, we show that this problem can be reduced to the global maximization of a concave function over a convex set, or alternatively, to the global minimization of a convex program w...

The nonconvex and nonsmooth optimization problem has been attracting increasing attention in recent years image processing machine learning research. algorithm-based reweighted step widely used many applications. In this paper, we propose a new, extended version of the iterative convex majorization–minimization method (ICMM) for solving minimization problem, which involves famous methods. To pr...

Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Th...

This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional fu...

In order for primal-dual methods to be applicable to a constrained minimization problem, it is necessary that restrictive convexity conditions are satisfied. In this paper, we consider a procedure by means of which a nonconvex problem is convexified and transformed into one which can be solved with the aid of primal-dual methods. Under this transformation, separability of the type necessary for...

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the refe...

Based on the well-known result that the sum of the largest eigenvalues of a symmetric matrix can be represented as a semidefinite programming problem (SDP), we formulate the nearest low-rank correlation matrix problem as a nonconvex SDP and propose a numerical method that solves a sequence of least-square problems. Each of the least-square problems can be solved by a specifically designed semis...

We consider a Cauchy problem associated to a nonconvex differential inclusion with ”maxima” and we prove a Filippov type existence result. This result allows to obtain a relaxation theorem for the problem considered.