A well-known approach to the design of computationally efficient filters is to use spectral factorization, i.e. a decomposition of a filter into a sequence of sub-filters. Due to the sparsity of the sub-filters, the typical processing speedup factor is within the range 1-10 in 2D, and for 3D it achieves 10-100. The design of such … Read more
The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. In this article, we propose an outer approximation algorithm for maximizing a function $h(x) = \varphi(f(x))$ over the efficient set $X_E$ of the bi-criteria convex programming problem $ {\rm Vmin} \{f(x)=(f_1(x), f_2(x))^T … Read more
We consider the problem of minimizing a continuously di erentiable function of several variables subject to simple bound and general nonlinear inequality constraints, where some of the variables are restricted to take integer values. We assume that the rst order derivatives of the objective and constraint functions can be neither calculated nor approximated explicitly. This class … Read more
Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate … Read more
This paper studies the solution of two problems—bound-constrained quadratic programs and linear complementarity problems—by two-phase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions than those assumed for other methods in the literature. The active set prediction phase employs matrix splitting iterations … Read more
It is well-known that the search direction generated by the standard (unmodified) PRP nonlinear conjugate gradient method is not necessarily a descent direction of the objective function, which brings difficulty for its global convergence for general functions. However, to our surprise, it is easily proved in this short note that the unmodified PRP method still … Read more
The document describes COIN-OR METSlib, a C++ framework for local search based metaheuristics. METSlib has been used to implement a massively parallel VRP algorithm, a state of the art Vertex Coloring Problem solver, a Timetabling software, and in many other projects. ArticleDownload View PDF
We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing theory. … Read more
This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are … Read more
In this work we consider the symmetric network equilibrium problem formulated as convex minimization problem whose variables are the path flows. In order to take into account the difficulties related to the large dimension of real network problems we adopt a column generation strategy and we employ a gradient projection method within an inexact decomposition … Read more