This article considers the minimum sum-of-squares clustering (MSSC)problem. The mathematical modeling of this problem leads to a min − sum −min formulation which, in addition to its intrinsic bi-level nature, has the significant characteristic of being strongly nondifferentiable. To overcome these difficulties, the proposed resolution method, called Hyperbolic Smoothing, adopts a smoothing stra...

The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. The well-studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods such as BFGS have been used directly to obtain globally convergent methods. S...

The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix under the Frobenius norm. The well studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods like BFGS have been used directly to obtain globally convergent methods. S...

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.

We study the worst case complexity of computing ε-approximations of surface integrals. This problem has two sources of partial information: the integrand f and the function g defining the surface. The problem is nonlinear in its dependence on g. Here, f is an r times continuously differentiable scalar function of l variables, and g is an s times continuously differentiable injective function of...

Abstract The paper concerns boundary value problems for general nonautonomous first-order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right-hand sides are small. In case all data of problem almost periodic, we prove bounded solution is also periodic. For nonhomogeneous version linearized problem, provide stable dissipativity condit...

We consider the following classes of nonlinear programming problems: the minimization of smooth functions subject to general constraints and simple bounds on the variables; the noniinear l~problem; and the minimax problem. Numerically reliable methods for solving problems in each of these classes, based upon exploiting the structure of the problem in constructing simple differentiable penalty f...