tradeoff based decomposition and decision making in multiobjective programming to facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision making a multiobjective decomposition scheme is proposed that restructures the original problem as a collection of smaller sized subproblems with only subsets of the original criteria a priori preferences on objective tradeoffs are integrated into this process by modifying the ordinary pareto order by more general domination cones and decision makers are supported by an interactive decision making procedure to coordinate any remaining tradeoffs using concepts of approximate efficiency a theoretical foundation for this method is provided and an illustrative application to multiobjective portfolio optimization is described in detail

approximation of pareto optima in multiple objective shortest path problems we study methods for approximating the set of pareto optimal paths in multiple objective shortest path problems known generalizations of standard shortest path methods will compute this set but can suffer from rapidly increasing computational and storage demands as problem size increases in an effort to avoid such difficulties we develop approximation methods that can estimate the pareto optima to any required degree of accuracy the approximation methods are fully polynomial that is they operate in time and space bounded by a polynomial in problem size and accuracy of approximation the greater the accuracy the more time required to reach a solution we show how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of np complete single objective problems

recursive estimation methods for discrete systems in system identification the error evolution is composed of two decoupled parts one is the identifying information on the current estimation residual while the other is past arithmetic errors previous recursive algorithms only considered how to update current prediction errors up to now research has mostly been based on recursive least squares rls methods in this note a general recursive identification method is proposed for discrete systems using this new algorithm a recursive empirical frequency domain optimal parameter refop estimate is established the refop method has the advantage of resisting disturbance noise some simulations are included to illustrate the new method s reliability

preference structure representation using convex cones in multicriteria integer programming a new efficient system of representing the decision maker s preference structure in solving multicriteria integer programming problems is developed the problem is solved by an interactive branch and bound method that employs the procedure of zionts and wallenius zionts s j wallenius 1983 an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions management sci 295 for multicriteria linear programming the decision maker s underlying utility function is assumed to be pseudoconcave and his pairwise comparisons of decision alternatives are used to determine his preference structure in terms of certain convex cones in the objective function space and constraints on the weights on the objectives in the weight space the two forms of preference structure representation are interrelated and their underlying theory is developed the primary objective of a representation scheme is exactness and in this respect it is shown that the constraints on the weights are not adequate for representing nonlinear utility functions on the other hand the convex cones exactly represent any quasiconcave utility function and clearly avoid the approximations and inaccuracies in other utility assessment systems accordingly an efficient ordered representation using convex cones is developed an algorithmic framework for multicriteria integer programming that integrates the representation using convex cones with the branch and bound solution procedure is developed computational experience with bicriteria problems having up to 80 variables and 40 constraints is presented

the utility efficient set and its interactive reduction we assume a decision situation under risk with incomplete information on preferences modelled as a vector utility function we consider an additive aggregation of its components and partial information on the scaling constants we develop the concept of utility efficiency to identify efficient strategies in discrete problems when the information about the scaling constants of the decision maker is in the form of a polyhedral cone a characterization of the utility efficient set provides a practical way to compute such efficient strategies we then discuss an interactive method based on the assessment of the scaling constants via an interactive paired comparison with its convergence the method is complemented by a procedure to reduce the utility efficient set to aid in the process of reaching a final strategy

adaptive linear filtering using interior point optimization techniques we propose a novel approach for the linear adaptive filtering problem using techniques from interior point optimization the main idea is to formulate a feasibility problem at each iteration and obtain as an estimate a filter near the center of the feasible region it is shown under some mild conditions that this algorithm generates a sequence of filters converging to the optimum linear filter at the rate o 1 n where n is the number of data samples furthermore we show that the algorithm can be made recursive with a per sample complexity of o m sup 2 3 where m is the filter length the potential of the algorithm for practical applications is demonstrated via numerical simulations where the new algorithm is shown to have superior transient behavior and improved robustness to the source signal statistics when compared to the recursive least squares rls method

inferring preferences in multiple criteria decision analysis using a logistic regression model a method is proposed for the analysis of multiple criteria decision making problems in an interactive environment when decision maker preferences are inconsistent with a simple utility model and or are self inconsistent e g showing intransitivities a maximum likelihood estimation procedure is invoked which is based on a logistic regression model relating the probability of selecting one decision option over another to a linear function of attribute values the method is illustrated by application to multi objective linear programming where it serves as an alternative to the method of zionts and wallenius zionts s j wallenius 1976 an interactive programming method for solving the multiple criteria problem management sci 22 652 663 and allows for inconsistencies which are not satisfactorily handled in the zionts wallenius approach

the homotopy theory of fusion systems the main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p completed classifying spaces of finite groups these spaces occur as the classifying spaces of certain algebraic objects which we call p local finite groups a p local finite group consists roughly speaking of a finite p group s and fusion data on subgroups of s encoded in a way explained below our starting point is our earlier paper blo on p completed classifying spaces of finite groups together with the axiomatic treatment by lluis puig pu pu2 of systems of fusion among subgroups of a given p group the p completion of a space x is a space xp which isolates the properties of x at the prime p and more precisely the properties which determine its mod p cohomology for example a map of spaces x f y induces a homotopy equivalence xp y p if and only if f induces an isomorphism in mod p cohomology and h xp fp h x fp in favorable cases if x is p good when g is a finite group the p completion bgp of its classifying space encodes many of the properties of g at p for example not only the mod p cohomology of bg but also the sylow p subgroup of g together with all fusion among its subgroups are determined up to isomorphism by the homotopy type of bgp our goal here is to give a direct link between p local structures and homotopy types which arise from them this theory tries to make explicit the essence of what it means to be the p completed classifying space of a finite group and at the same time yields new spaces which are not of this type but which still enjoy most of the properties a space of the form bgp would have we hope that the ideas presented here will have further applications and generalizations in algebraic topology but this theory also fits well with certain aspects of modular representation theory in particular it may give a way of constructing classifying spaces for blocks in the group ring of a finite group over an algebraically closed field of characteristic p a saturated fusion system f over a p group s consists of a set homf p q of monomorphisms for each pair of subgroups p q s which form a category under composition include all monomorphisms induced by conjugation in s and satisfy certain other axioms formulated by puig definitions 1 1 and 1 2 below in particular these axioms are satisfied by the conjugacy homomorphisms in a finite group we refer to pu and pu2 for more details of puig s work on saturated

fusion systems and constructing free actions on products of spheres we show that every rank two p group acts freely and smoothly on a product of two spheres this follows from a more general construction given a smooth action of a finite group g on a manifold m we construct a smooth free action on m times mathbb s n 1 times dots times mathbb s n k when the set of isotropy subgroups of the g action on m can be associated to a fusion system satisfying certain properties another consequence of this construction is that if g is an almost extra special p group of rank r then it acts freely and smoothly on a product of r spheres

interior point least squares estimation transient convergence analysis and application to mmse decision feedback equalization in many communication systems training sequences are used to help the receiver identify and or equalize the channel the amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization in this paper we propose the use of a new adaptive filtering method called interior point least squares ipls for adaptive equalization first we show that ipls converges exponentially fast in the transient phase then we use the ipls algorithm to update the weight vector for a minimum mean square error decision feedback equalizer mmse dfe in a cdma downlink scenario numerical simulations show that when training sequences are short ipls consistently outperforms rls in terms of system bit error rate and packet error rate as the training sequence gets longer ipls matches the performance of the rls algorithm

low complexity constrained affine projection algorithms this paper proposes low complexity constrained affine projection cap algorithms the algorithms are suitable for linearly constrained filtering problems often encountered in communications systems the cap algorithms derived in this paper trade convergence speed and computational complexity in the same way as the conventional affine projection ap algorithm in addition data selective versions of the cap algorithm are derived based on the concept of set membership filtering the set membership constrained affine projection sm cap algorithms include several constraint sets in order to construct a space of feasible solutions for the coefficient updates the sm cap algorithms include a data dependent step size that provides fast convergence and low mean squared error the paper also discusses important aspects of convergence and stability of constrained normalized adaptation algorithms and shows that normalization may introduce bias in the final solution

nonlinear multiple objective optimization an algorithm and some theory this paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using zionts wallenius type of interaction the zionts wallenius method as extended in this paper can be used for solving multiple criteria problems with concave objective and implicit value functions and convex feasible regions modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed

hierarchical multi objective decision making this paper proposes a hierarchical procedure for solving decision problems with multiple objectives the procedure consists of two levels a top and a base level the main idea is that the top level only provides general preference information taking this information into account the base level then determines a compromise solution for a multi objective linear program it will be shown how such a hierarchical procedure can be structured by deriving weight restrictions from the general preference information of the top level and by using the interactive modm procedure of zionts and wallenius on the base level

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

a combined tchebycheff aspiration criterion vector interactive multiobjective programming procedure in this paper we combine the tchebycheff method of steuer and choo with wierzbicki s aspiration criterion vector method in order to form an improved procedure for interactive multiple objective programming the combined procedure is sensible because the tchebycheff and aspiration criterion vector methods possess complementary distinguishing characteristics solve similar optimization problems to probe the nondominated set and share a similar computer user interface in the early iterations tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search in later iterations aspiration criterion vector probes might be used to pinpoint a final solution computational experience is reported showing the improved effectiveness of the combined procedure when employed in this fashion when compared against the tchebycheff and aspiration criterion vector methods run separately

cut a multicriteria approach for concavifiable preferences we consider the problem of helping a decision maker dm choose from a set of multiattributed objects when her preferences are concavifiable i e representable by a concave value function we establish conditions under which preferences or preference intensities are concavifiable we also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the dm this can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure we report on the practical use of this procedure with several dms for a flat choice problem and its computational performance on a set of project portfolio selection problem instances the use of preference intensities is found to provide significant improvements to the performance of the procedure

periodic complexes and group actions in this paper we show that the cohomology of a connected cw complex is periodic if and only if it is the base space of a spherical fibration with total space that is homotopically finite dimensional as applications we characterize those discrete groups that act freely and properly on in x sm we construct nonstandard free actions of rank two simple groups on finite complexes y sn x sm and we prove that a finite p group p acts freely on such a complex if and only if it does not contain a subgroup isomorphic to z p 3

free actions of finite groups on s n x s n let p be an odd prime we construct a non abelian extension of s by z p z p and prove that any finite subgroup of acts freely and smoothly on s2p 1 s2p 1 in particular for each odd prime p we obtain free smooth actions of infinitely many non metacyclic rank two p groups on s2p 1 s2p 1 these results arise from a general approach to the existence problem for finite group actions on products of equidimensional spheres

multiplicative decision rules for multiobjective decision problems abstract properties of consistency of general decision rules for multiobjective decision problems are discussed decision rules based on the family of weighted geometric averages are introduced their properties are analysed and possible implementations are discussed

on the basis of the burnside ring of a fusion system abstract we consider the burnside ring a f of f stable s sets for a saturated fusion system f defined on a p group s it is shown by s p reeh that the monoid of f stable sets is a free commutative monoid with canonical basis p we give an explicit formula that describes p as an s set in the formula we use a combinatorial concept called broken chains which we introduce to understand inverses of modified mobius functions

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

a comparative study of interactive tradeoff cutting plane methods for momp abstract in this paper four interactive cutting plane methods developed for multiple objective mathematical programming problems are compared to one another using randomly selected problems tradeoff cutting plane methods converge to the best compromise solution by iteratively reducing the objective space by cutting planes the cutting planes are constructed using partial preference information obtained from the decision maker the performance of the four methods is evaluated and compared to one another by solving the test problems under i four classes of preference functions in addition to the original preference functions to simulate the nonexisting decision maker ii different precision levels in the decision maker s comparative accuracy iii decision space expanded or contracted and iv inconsistent responses by the decision maker based on the comparative study some guidelines for performing a comparative study of multicriteria interactive methods are presented

an interactive weight space reduction procedure for nonlinear multiple objective mathematical programming to make a decision that is defined by multiple conflicting objectives it is necessary to know the relative importance of the different objectives in this paper we present an interactive method and the underlying theory for solving multiple objective mathematical programming problems defined by a convex feasible region and concave continuously differentiable objective functions the relative importance of the different objectives for a decision maker is elicited by using binary comparisons of objective function vectors the method is cognitively easy to use and in test problems has rapidly converged to an optimal solution

a comparison of two reference point methods in multiple objective mathematical programming abstract when making decisions with multiple criteria a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria in multiple objective mathematical programming solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions these reference point solution methods commonly use a scalarizing function that reaches down from the ideal solution in a direction specified by the aspiration point conversely a similar scalarizing function can push out from the nadir point toward a specified aspiration point these scalarizing functions are similar in structure but diametrically opposed in their reference points in this paper we examine how these approaches behave from a technical point of view and conduct an experiment to understand better the human behaviour of users of these approaches insights we gain on the evenness of dispersion are relevant when attempting to construct a representation of the nondominated set further the technical characteristics of the two formulations solutions combined with behavioural tendencies allow us to comment on the implications for their use in interactive multiple objective methods

dual cone approach to convex cone dominance in multiple criteria decision making abstract in a paper published in management science in 1984 korhonen wallenius and zionts presented the idea and method based on convex cone dominance in the discrete multiple criteria decision making framework in our current paper we revisit the old idea from a new standpoint and provide the mathematical theory leading to a dual cone based approach to solving such problems our paper makes the old results computationally more tractable the results provided in the present paper also help extend the theory

a multiobjective discrete optimization model for land allocation a multiobjective integer programming model is presented for allocating an area of land for development the objectives considered in the allocation are cost proximity to desirable and undesirable land features and the shape of the area an interactive multiobjective optimization algorithm is presented and applied to the model the algorithm generates a subset of efficient solutions with some guidance from the decision maker at each iteration as to what constitutes a preferred efficient point the algorithm calls for the frequent solution of subproblems which constrain all but one of the objectives while optimizing the remaining one in the land allocation model the subproblems are integer programs solved efficiently by specialized enumeration techniques for some of the subproblems namely those using proximity as the single objective the first feasible solution we enumerate is guaranteed optimal for the other subproblems we show that an algorithm with this fortunate property would require the solution of an np hard problem at each step of the enumeration the model and algorithm were tested in locating potential sites for a 13 acre residential development within a 2250 acre study area near norris tennessee

study of the transient phase of the forgetting factor rls we investigate the convergence properties of the forgetting factor rls algorithm in a stationary data environment using the settling time as our performance measure we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level specifically when the observation noise level is low high snr rls when initialized with a matrix of small norm it has an exceptionally fast convergence convergence speed decreases as we increase the norm of the initialization matrix in a medium snr environment the optimum convergence speed of the algorithm is reduced as compared with the previous case however rls becomes more insensitive to initialization finally in a low snr environment we show that it is preferable to initialize the algorithm with a matrix of large norm

a review of interactive methods for multiobjective integer and mixed integer programming this paper makes a review of interactive methods devoted to multiobjective integer and mixed integer programming moip momip problems the basic concepts concerning the characterization of the non dominated solution set are first introduced followed by a remark about non interactive methods vs interactive methods then we focus on interactive moip momip methods including their characterization according to the type of preference information required from the decision maker the computing process used to determine non dominated solutions and the interactive protocol used to communicate with the decision maker we try to draw out some contrasts and similarities of the different types of methods

testing the efficiency of pairwise comparison methods in discrete multiple criteria problems we test the efficiency of two pairwise comparison methods the methods studied are salminen s piecewise linear prospect theory plp method and the convex cone method by korhonen wallenius and zionts kwz the plp method is based on a piecewise linear difference function the kwz method assumes a quasi concave utility or value function these methods are tested using randomly generated data sets with 50 100 150 and 200 alternatives and from 2 up to 6 criteria the dm s preference statements are simulated using linear quadratic and chebycheff value functions and piecewise linear difference functions both methods lose their efficiency very rapidly with increasing number of criteria our results indicate that pairwise comparison methods are not as efficient as reported in literature

use of convex cones in interactive multiple objective decision making one approach for solving decision problems involving multiple objectives is interactive optimization methods based on this approach assess the decision maker s preference structure interactively typically based on pairwise comparisons and tradeoffs and guide the search process toward identifying improved solutions a desirable feature of such approaches that is based on minimizing the preference information requirements is fast convergence toward this end the use of convex cones as a preference structure representation has been proposed in the literature in this work new theory is developed that aids in further reducing preference information requirements and improving convergence new cones termed p cones are developed the efficiencies of solution alternatives are evaluated with respect to the p cones and these are termed p cone efficiencies acceleration and early termination procedures that are based on these efficiencies are proposed the procedures are presented within a solution framework for solving multiple objective linear programming molp problems along with computational results

graphically structured value function compilation classical work on eliciting and representing preferences over multi attribute alternatives has attempted to recognize conditions under which value functions take on particularly simple and compact form making their elicitation much easier in this paper we consider preferences over discrete domains and show that for a certain class of simple and intuitive qualitative preference statements one can always generate compact value functions consistent with these statements these value functions maintain the independence structure implicit in the original statements for discrete domains these representation theorems are much more general than previous results however we also show that it is not always possible to maintain this compact structure if we add explicit ordering constraints among the available outcomes

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

tradeoff directions in multiobjective optimization problems multiobjective optimization problems mop typically have conflicting objectives wherein a gain in one objective is at the expense of another tradeoff directions which measure the change in some objectives relative to changes in others provide important information as to the best direction of improvement from the current solution in this paper we present a general definition of tradeoffs as a cone of directions and provide a general method of calculating tradeoffs at every pareto optimal point of a convex mop this extends current definitions of tradeoffs which assume certain conditions on the feasible set and the objective functions two comprehensive numerical examples are provided to illustrate the tradeoff directions and the methods used to calculate them