variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

consequences of dropping nonessential objectives for the application of mcdm methods abstract in this article we consider the problem of nonessential objectives for multiobjective optimization problems mop with linear objective functions in 1977 an approach based on the reduction of size of the matrix of objective functions has been worked out by one of the present authors gal t leberling h 1977 european journal of operations research 1 176 184 although this method for dropping nonessential objectives leads to a mathematically equivalent mop problems concerning the application of mop methods may arise for instance dropping some or all of the nonessential objectives the question is how to ensure obtaining the same solution as with all objectives involved we consider the problem of adapting the parameters of multiobjective optimization methods for the case of weighting methods a simple procedure for adapting the weights is analyzed for other methods e g reference point approaches such a simple possibility for adapting the parameters is not given

on efficient solutions to multiple objective mathematical programs this note develops properties of quasi efficient solutions and explores interrelationships to the classical concept of efficiency in particular a point is a quasi efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives this result is then used to characterize the set of quasi efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives

a new stage structured predator prey gomportz model with time delay and impulsive perturbations on the prey abstract in this paper we formulate a robust prey dependent consumption predator prey gomportz model with periodic harvesting catching or poisoning for the prey and stage structure for the predator with constant maturation time delay through stage time delay and perform a systematic mathematical and ecological study by use of the discrete dynamical system determined by the stroboscopic map we obtain a predator extinction periodic solution further we show it is globally attractive when some parameters of the system are under appropriate conditions by using the theory on delay functional and impulsive differential equation we obtain sufficient condition with time delay for the permanence of the system in this paper the main feature is that we introduce time delay and pulse into the predator prey natural enemy pest model with stage structure exhibit a new modeling method which is applied to investigate delay impulsive differential equations and give some reasonable suggestions for pest management

on min norm and min max methods of multi objective optimization this paper examines pareto optimality of solutions to multi objective problems scalarized in the min norm compromise programming generalized goal programming or unrestricted min max formulations issues addressed include among others uniqueness in solution or objective space penalization for over achievement of goals min max reformulation of goal programming inferiority in tchebycheff norm minimization strength and weakness of weighted bound optimization quasi satisficing decision making just attaining or even over passing the goals trading off by modifying weights or goals non convex pareto frontier new general necessary and sufficient conditions for both pareto optimality and weak pareto optimality are presented various formulations are compared in theoretical performance with respect to the goal point location ideas for advanced goal programming and interactive decision making are introduced

simpson points in planar problems with locational constraints the polyhedral gauge case in this paper we address the problem of finding simpson points in planar models with locational constraints when distances are measured by polyhedral gauges making use of the results we have stated in a previous paper we show here the existence of a finite set of points in the plane independent of the weights associated with the users that contains at least a simpson point connection between simpson points as a result of a voting process and weber points as the outcome of a planning process are explored it is shown by means of an example that the existing relations for the unconstrained case are no longer true when locational constraints are imposed in order to reconcile both voting and planning processes a biobjective problem is described for which we construct a finite dominating set

global stability of a lotka volterra type predator prey model with stage structure and time delay a delayed lotka volterra type predator prey model with stage structure for predator is investigated it is assumed in the model that the individuals in the predator population may belong to one of two classes the immatures and the matures the age to maturity is presented by a time delay and that the immature predators do not have the ability to prey by analyzing characteristic equations and using an iterative technique a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model numerical simulations are carried out to illustrate the validity of our results

the matrix sign decomposition and its relation to the polar decomposition the sign function of a square matrix was introduced by roberts in 1971 we show that it is useful to regard s sign a as being part of a matrix sign decomposition a sn where n a2 1 2 this decomposition leads to the new representation sign a a a2 1 2 most results for the matrix sign decomposition have a counterpart for the polar decomposition a uh and vice versa to illustrate this we derive best approximation properties of the factors u h and s determine bounds for a s and a u and describe integral formulas for s and u we also derive explicit expressions for the condition numbers of the factors s and n an important equation expresses the sign of a block 2 2 matrix involving a in terms of the polar factor u of a we apply this equation to a family of iterations for computing s by pandey kenney and laub to obtain a new family of iterations for computing u the iterations have some attractive properties including suitability for parallel computation

the iterative methods for computing the polar decomposition of rank deficient matrix some iterative methods for computing the polar decomposition are introduced they can be used to compute the polar decomposition of rank deficient matrix which includes both square and rectangular matrices a very important application of the polar decomposition is about matrix sign function through the methods of this paper to compute the matrix sign function is convenient some examples are provided in this paper

approximating combinatorial optimization problems with the ordered weighted averaging criterion abstract this paper deals with combinatorial optimization problems with k cost scenarios inducing k linear objectives the popular ordered weighted averaging owa criterion is used to aggregate the objectives and compute a solution it is well known that minimizing owa for most basic combinatorial problems is weakly np hard even if the number of scenarios k equals two and strongly np hard when k is a part of the input in this paper the problem with nonincreasing weights in the owa criterion and a large k is first considered a method of reducing the number of scenarios by appropriately aggregating the costs before solving the problem is proposed it is shown that an optimal solution to the reduced problem has a guaranteed worst case approximation ratio some new approximation results for the hurwicz criterion which is a special case of owa are also presented

pareto optima of isostatic trusses abstract multicriterion optimization of elastic stress limited isostatic trusses is considered and a numerical method for determining the pareto optimal set of the problem is developed the weight of the structure and some chosen nodal displacements are taken as design criteria and member areas are used as design variables the corresponding bicriterion problem with weight and one displacement in the objective function is solved exactly and this result is used as a basis of the proposed method by introducing certain parameters each joined with one displacement criterion the pareto optimal solutions of the general problem may be obtained with any accuracy two examples are given to illustrate the method

approximating the pareto optimal set using a reduced set of objective functions real world applications of multi objective optimization often involve numerous objective functions but while such problems are in general computationally intractable it is seldom necessary to determine the pareto optimal set exactly a significantly smaller computational burden thus motivates the loss of precision if the size of the loss can be estimated we describe a method for finding an optimal reduction of the set of objectives yielding a smaller problem whose pareto optimal set w r t a discrete subset of the decision space is as close as possible to that of the original set of objectives utilizing a new characterization of pareto optimality and presuming a finite decision space we derive a program whose solution represents an optimal reduction we also propose an approximate computationally less demanding formulation which utilizes correlations between the objectives and separates into two parts numerical results from an industrial instance concerning the configuration of heavy duty trucks are also reported demonstrating the usefulness of the method developed the results show that multi objective optimization problems can be significantly simplified with an induced error which can be measured

norm methods and partial weighting in multicriterion optimization of structures methods for generating pareto optimal solutions to a multicriterion optimization problem are considered the norm methods based on the scalarization of the original multicriterion problem by using the l norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested in addition an alternative approach which instead of scalarization reduces the dimension of the multicriterion problem is proposed this is called the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted sum of the criteria is used as the objective function the first of these two approaches norm method is very flexible from a designer s point of view and it can be applied also in non convex cases to the determination of the pareto optimal set whereas the latter partial weighting method is especially suitable for problems where the number of criteria is large throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design

minimizing the area of a pareto confidence region abstract a constrained optimization problem is formulated and solved in order to determine the smallest confidence region for the parameters of the pareto distribution in a proposed family of sets the objective function is the area of the region whereas the constraints are related to the required confidence level explicit expressions for the area and confidence level of a given region are first deduced an efficient procedure based on minimizing the corresponding lagrangian function is then presented to solve the nonlinear programming problem the process is valid when some of the smallest and largest observations have been discarded or censored i e both single right or left and double censoring are allowed the optimal pareto confidence region is derived by simultaneously solving three four nonlinear equations in the right double censoring case in most practical situations newton s method with the balanced set as the starting point only needs a few iterations to find the global solution in general the reduction in area of the optimal pareto region with respect to the balanced set is considerable if the sample size n is small or moderately large which is usual in practice this reduction is sometimes impressive when n is quite small and the censoring degree is fairly high two numerical examples regarding component lifetimes and fire claims are included for illustrative and comparative purposes

interdependence in fuzzy multiple objective programming abstract in multiple objective programs mop application functions are establised to measure the degree of fulfillment of the decision maker s requirements achievement of goals nearness to an ideal point satisfaction etc about the objective functions see e g delgado et al 1990 zimmermann 1978 and are extensively used in the process of finding good compromise solutions we have earlier demonstrated that the use of interdependences among objectives of a mop in the definition of the application functions provides for more correct solutions and faster convergence in this paper generalizing the principle of application functions to fuzzy multiple objective programs fmop with interdependent objectives we define a large family of application functions for fmop and illustrate our ideas by a simple three objective program

a sixth order iterative method for approximating the polar decomposition of an arbitrary matrix a new iterative method for computing the polar decomposition of any rectangular complex matrix is presented and analyzed the study of the convergence shows that this method has order of convergence six some numerical tests confirm the theoretical results and allow us to compare the proposed iterative scheme with other known ones

persistence of some stage structured ecosystems with finite and infinite delay abstract the persistence of some stage structured predator prey model with finite and infinite delay was studied in this paper by analyzing right hand functions and using the comparison theorem some sufficient conditions for the persistence of populations with finite and infinite delay were derived

relational systems of preference with one or more pseudo criteria some new concepts and results this paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory sections 1 3 present four fundamental situations of preferences their combinations and the concept of relational system of preferences in 4 a particular case of relational system of preference is studied it is associated with the concept of pseudo criterion derived from the classical concept of criterion by adjunction of two thresholds some results are given generalizing the properties of such well known structures as complete preorders and semiorders sections 5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account

multiobjective optimization of large scale structures this paper presents a multiobjective optimization algorithm based on generalized compound scaling techniques the algorithm handles any number of objective functions similar to handling behavior constraints this technique generates a partial pareto set while solving the optimization problem a reliability ba sed decision criterion is used for selecting the best compromise design the example cases considered in this work include various disciplines in airframe structures such as stress displacement and frequency with hundreds of design variables and constraints this paper also discusses the concept of pareto optima l solutions in the context of a multiobjective structural optimization problem and the commonly used methods of generating pareto optimal solutions

objective space partitioning using conflict information for solving many objective problems we present an algorithm that partitions the objective space based on an analysis of the conflict information obtained from the current pareto front approximation by partitioning the objectives in terms of the conflict among them we aim to separate the multiobjective optimization into several subproblems in such a way that each of them contains the information to preserve as much as possible the structure of the original problem we implement this framework by performing ranking and parent selection independently in each subspace our experimental results show that the proposed conflict based partition strategy outperforms a similar algorithm in a test problem with independent groups of objectives in addition the new strategy achieves a better convergence and distribution than that produced by a strategy that creates subspaces at random in problems in which the degree of conflict among the objectives is significantly different the conflict based strategy presents a better performance

nonessential objectives within network approaches for mcdm in gal and hanne eur j oper res 119 1999 373 the problem of using several methods to solve a multiple criteria decision making mcdm problem with linear objective functions after dropping nonessential objectives is analyzed it turned out that the solution does not need be the same when using various methods for solving the system containing the nonessential objectives or not in this paper we consider the application of network approaches for multicriteria decision making such as neural networks and an approach for combining mcdm methods called mcdm networks we discuss questions of comparing the results obtained with several methods as applied to the problem with or without nonessential objectives especially we argue for considering redundancies such as nonessential objectives as a native feature in complex information processing in contrast to previous results on nonessential objectives the current paper focuses on discrete mcdm problems which are also denoted as multiple attribute decision making madm