Global Optimization Criterion Research Articles

Fast detection of the first zero-crossing in a measurement signal set

In this paper the problem of finding the first from the left zero crossing point among N signals over a fixed time interval is considered. This problem arises in the non-parametric identification of special signals, in the Wavelet transform and image processing. To solve this problem, this paper proposes a new method based on global optimization criteria. Numerical experiments executed with a set of real practical problems demonstrate quite satisfactory performances of the proposed algorithms.

Global Optimality Criterion and a Duality with a Zero Gap in Nonconvex Optimization

This paper presents a relation between geometrical criteria for optimality and a duality in two nonconvex problems: a quasi-convex maximization over a convex set, and a general minimization over the complement of a convex set. A connection between the duality by Toland, the global optimality criterion by Hiriart-Urruty, and the author's result is also given. Several applications are presented.

A Global Optimization Algorithm for Concave Quadratic Programming Problems

Using a global optimality criterion for concave quadratic problems due to Hiriart–Urruty and Lemaréchal, the authors present an algorithm which manages to “escape” from a local solution and lead towards the global one. In addition, this procedure recognizes the unsolvability of the problem (due to unboundedness of the objective function on the feasible region) and also generates an improving feasible direction even if the starting point does not satisfy the Karush/Kuhn/Tucker conditions. As a key subroutine, a recursive procedure will be used which determines whether or not a given symmetric $n \times n$-matrix is copositive, i.e., yields a quadratic form that is positive on a given polyhedral cone. Both this subroutine and the main body of the algorithm frequently employ the simplex method, while all other operations are elementary.

Flexibility of scheduling tools for order production problems

A fundamental issue in scheduling tools for order production systems is the trade-off between the feasibility of a solution with respect to a set of dynamic local constraints and the evaluation of a schedule with respect to different global optimality criteria. CIM managers clamour for more flexible and easy to handle tools than those provided by classical scheduling theory. Decision Support Systems (DSS) have been proved to be valuable tools for manipulating schedules and for managing information on the production process. This paper surveys previous work on scheduling in production systems, and presents a methodology for facing production scheduling problems. New design criteria and interactive models for effectively supporting the methodology in flexible and dynamic production environments are discussed.

Using copositivity for global optimality criteria in concave quadratic programming problems

In this note we specify a necessary and sufficient condition for global optimality in concave quadratic minimization problems. Using this condition, it follows that, from the perspective of worst-case complexity of concave quadratic problems, the difference between local and global optimality conditions is not as large as in general. As an essential ingredient, we here use thee-subdifferential calculus via an approach of Hiriart-Urruty and Lemarechal (1990).

The relief indicator method for constrained global optimization

We consider the problem of globally minimizing a continuous, not-necessarily smooth function f(x) over a compact set S in Rn. To each real number α we associate a function φα(x), called the relief indicator, such that the function φαα(x) + ∥x∥2 is closed, convex, and a feasible point x is a global optimal solution if and only if 0 = min{φα(x): x ∈ Rn}, where α = f(x). Based on this global optimality criterion, an algorithm is then developed which reduces the problem to a sequence of linearly constrained concave quadratic separable programs. We discuss the practical use of these results when n (the number of variables) is small and also show how the method can be applied in the decomposition of certain nonconvex problems.

A connectionist model for diagnostic problem solving

A competition-based connectionist model for solving diagnostic problems is described. The problems under consideration are computationally difficult in that multiple disorders may occur simultaneously and a global optimum in the space exponential to the total number of possible disorders is sought as a solution. To solve this problem, global optimization criteria are decomposed into local optimization criteria that are used to govern node activation updating in the connectionist model. Nodes representing disorders compete with each other to account for each 'individual' present manifestation, yet complement each other to account for all present manifestation, yet complement each other to account for all present manifestations through parallel node interactions. When equilibrium is reached, the network settles into a locally optimal state in which some disorder nodes (winners) are fully activated and compose the diagnosis for the given case, while all other disorder nodes are fully deactivated. A resettling process is proposed to improve accuracy. Three randomly generated examples of diagnostic problems, each of which has 1024 cases, were tested.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain

An estimation approach is described for three-dimensional reconstruction from line integral projections using incomplete and very noisy data. Generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain. The object models, a statistical measurement model, and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem. For computational feasibility, a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion. The formulation and algorithm are restricted to objects whose center axis is a single-valued function of a fixed spatial coordinate. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135 degrees sector, at an average signal-to-noise ratio of 3.3. >

Closedness conditions for the optimality of a family of non-convex optimization problems

A global optimality criterion for a family of non-convex optimization problems is proved using a result of J. Dedieu [2] concerning the closedness of the image of a closed set by a multivalued function.