Given symmetric matrices B,D∈ℝ<Superscript> n×n </Superscript> and a symmetric positive definite matrix W∈ℝ<Superscript> n×n </Superscript>, maximizing the sum of the Rayleigh quotient <Emphasis Type="Bold">x <Superscript>⊤</Superscript> D <Emphasis Type="Bold">x and the generalized Rayleigh quotient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\frac{\mathbf{x}^{\top}B \mathbf{x}}{\vphantom{\mathrm{I}^{\mathrm{I}}}\mathbf{x}^{\top}W\mathbf{x} }$</EquationSource> </InlineEquation>...</equationsource></inlineequation></emphasis></superscript></emphasis></superscript></superscript>

We propose an iterative algorithm for the minimization of a ℓ <Subscript>1</Subscript>-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the...</subscript>

When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such...

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0≤u≤1 and ∫u=m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth...

Regularization methods for inverse problems formulated in Hilbert spaces usually give rise to over-smoothness, which does not allow to obtain a good contrast and localization of the edges in the context of image restoration. On the other hand, regularization methods recently introduced in Banach...

A globally convergent algorithm based on the stabilized sequential quadratic programming (sSQP) method is presented in order to solve optimization problems with equality constraints and bounds. This formulation has attractive features in the sense that constraint qualifications are not needed at...

This paper proposes a hybrid self-adaptive evolutionary algorithm for graph coloring that is hybridized with the following novel elements: heuristic genotype-phenotype mapping, a swap local search heuristic, and a neutral survivor selection operator. This algorithm was compared with the...

We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem and...

Many promising optimization algorithms for solving numerical optimization problems come from population-based metaheuristics. A few of them are based on Swarm-Intelligence Algorithms, which are inspired by the collective behavior of social organisms. One of the most successful of such...

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues...