new algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds there are many applications related to singly linearly constrained quadratic programs subjected to upper and lower bounds in this paper a new algorithm based on secant approximation is provided for the case in which the hessian matrix is diagonal and positive definite to deal with the general case where the hessian is not diagonal a new efficient projected gradient algorithm is proposed the basic features of the projected gradient algorithm are 1 a new formula is used for the stepsize 2 a recently established adaptive non monotone line search is incorporated and 3 the optimal stepsize is determined by quadratic interpolation if the non monotone line search criterion fails to be satisfied numerical experiments on large scale random test problems and some medium scale quadratic programs arising in the training of support vector machines demonstrate the usefulness of these algorithms

rational choice under fuzzy preferences the orlovsky choice function abstract there have been many different suggestions in the literature as to how to generate exact choices on the basis of fuzzy preferences this paper seeks to provide axiomatic support to one of these choice functions due to orlovsky it is shown that under a transitivity restriction independent of max min transitivity this choice function implies and is implied by a set of simple conditions

iterative methods for large convex quadratic programs a survey in this paper we give a state of the art review of many iterative methods for solving large convex quadratic programs we attempt to classify several of the more basic methods in two categories within each of which a unified iterative scheme will be introduced and its convergence analyzed hybrid iterative methods such as the proximal point algorithm and a diagonalization scheme that make use of the more basic schemes will also be described the results of an extensive computer experimentation which is aimed at comparing the relative performance of the various methods will be reported and discussed finally several important topics which require future research will be highlighted

a direct method for sparse least squares problems with lower and upper bounds a direct method is developed for solving linear least squares problems mathop min left ax b right 2 limits x wherea is large and sparse and the solution is subject to lower and upper boundsl x u the problem is initially transformed to upper triangular form by a sparseqr factorization an active set algorithm is then used the key step is the stable updating of ther factor associated with the columns ofa corresponding to the free variables when theq factor is not available for this a new method is developed which uses the semi normal equations and iterative refinement

a finite continuation algorithm for bound constrained quadratic programming the dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear ell 1 minimization problem with quadratic terms a smooth approximation to the linear ell 1 function is used to obtain a parametric family of piecewise quadratic approximation problems the unique path generated by the minimizers of these problems yields the solution to the original problem for finite values of the approximation parameter thus a finite continuation algorithm is designed results of extensive computational experiments are reported

a parallel relaxation method for quadratic programming problems with interval constraints abstract optimization problems with interval constraints are encountered in various fields such as network flows and computer tomography as these problems are usually very large they are not easy to solve without taking their sparsity into account recently row action methods which originate from the classical hildreth s method for quadratic programming problems have drawn much attention since they are particularly useful for large and sparse problems various row action methods have already been proposed for optimization problems with interval constraints but they mostly belong to the class of sequential methods based on the gauss seidel and sor methods in this paper we propose a highly parallelizable method for solving those problems which may be regarded as an application of the jacobi method to the dual of the original problems we prove convergence of the algorithm and report some computational results to demonstrate its effectiveness

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

degree of dominance and congruence axioms for fuzzy choice functions in this paper we introduce the degree of dominance of an alternative x with respect to an available fuzzy set of alternatives interpreting an available fuzzy set of alternatives as a criterion in decision making the degree of dominance establishes a hierarchy of alternatives with respect to this criterion with the degree of dominance new congruence axioms for fuzzy choice functions are formulated

a new index for bond management in an uncertain environment within the framework of assets liability management we understand that immunization is the main method to assure a certain yield in a future date departing from an initial portfolio although the objective of passive strategies is to design a portfolio that will achieve the performance of a predetermined benchmark active bond management strategies rely on expectations of interest rate movements or changes in yield spread relationships however the variation of the duration increases the risk of a portfolio that why the decision maker will have to choose the combination of expected return and risk which provides the higher utility finally the construction of a fuzzy return risk map will allow the decision maker to know the over risk and the over return as regards immunization strategy for each duration and for each risk aversion of the decision maker the construction of a risk return map presents the results in an appropriate way it will help the decision maker to choose the best duration for the decision maker interest rate forecast finally this methodology is applied to the spanish debt so that the decision maker can select the duration that brings him a greater preference

a cholesky dual method for proximal piecewise linear programming a quadratic programming method is given for minimizing a sum of piecewise linear functions and a proximal quadratic term subject to simple bounds on variables it may be used for search direction finding in nondifferentiable optimization algorithms an efficient implementation is described that updates a cholesky factorization of active constraints and provides good accuracy via iterative refinement numerical experience is reported for some large problems

a unified method for a class of convex separable nonlinear knapsack problems abstract in this paper a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems which are characterized by positive marginal cost pmc and increasing marginal loss cost ratio imlcr by taking advantage of these two characteristics the proposed algorithm is applicable to the problem with equality or inequality constraints in contrast to the methods based on karush kuhn tucker kkt conditions our approach has linear computation complexity numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems

data parallel quadratic programming on box constrained problems we develop designs for the data parallel solution of quadratic programming problems subject to box constraints in particular we consider the class of algorithms that iterate between projection steps that identify candidate active sets and conjugate gradient steps that explore the working space using the algorithm of more and toraldo report mcs p77 05 89 argonne national laboratory illinois 1989 as a specific instance of this class of algorithms we show how its components can be implemented efficiently on a data parallel simd computer architecture alternative designs are developed for both arbitrary unstructured hessian matrices and for structured problems implementations are carried out on a connection machine cm 2 they are shown to be very efficient achieving a peak computing rate over 2 gflops problems with several hundred thousand variables are solved within one minute of solution time on the 8k cm 2 extremely large test problems with up to 2 89 million variables are also solved efficie

on the convergence of interior reflective newton methods for nonlinear minimization subject to bounds we consider a new algorithm an interior reflective newton approach for the problem of minimizing a smooth nonlinear function of many variables subject to upper and or lower bounds on some of the variables this approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths reflection paths the interior reflective approach does not require identification of an activity set in this paper we establish that the interior reflective newton approach is globally and quadratically convergent moreover we develop a specific example of interior reflective newton methods which can be used for large scale and sparse problems

large correlation analysis in this paper a novel supervised dimensionality reduction method is developed based on both the correlation analysis and the idea of large margin learning the method aims to maximize the minimal correlation between each dimensionality reduced instance and its class label thus named as large correlation analysis lca unlike most existing correlation analysis methods such as cca ccas and cda which all maximize the total or ensemble correlation over all training instances lca devotes to maximizing the individual correlations between given instances and its associated labels and is established by solving a relaxed quadratic programming with box constraints experimental results on real world datasets from both uci and usps show its effectiveness compared to the existing canonical correlation analysis methods

rational fuzzy and sequential fuzzy choice in the setting of fuzzy choice theory we explore some relationships among known and new consistency axioms as well as consequences of rationalizability then we define the notion of sequential application of fuzzy choice functions and investigate its normative implications under related concepts of rationalizability in particular the fuzzy binariness axiom is verified by sequential fuzzy choice and the fuzzy arrow axiom when the set of alternatives is finite is preserved by the newly defined sequential procedure the latter property ensures that full rationality is preserved too

algorithms for the continuous nonlinear resource allocation problem new implementations and numerical studies patriksson 2008 provided a then up to date survey on the continuous separable differentiable and convex resource allocation problem with a single resource constraint since the publication of that paper the interest in the problem has grown several new applications have arisen where the problem at hand constitutes a subproblem and several new algorithms have been developed for its efficient solution this paper therefore serves three purposes first it provides an up to date extension of the survey of the literature of the field complementing the survey in patriksson 2008 with more then 20 books and articles second it contributes improvements of some of these algorithms in particular with an improvement of the pegging that is variable fixing process in the relaxation algorithm and an improved means to evaluate subsolutions third it numerically evaluates several relaxation primal and breakpoint dual algorithms incorporating a variety of pegging strategies as well as a quasi newton method our conclusion is that our modification of the relaxation algorithm performs the best at least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

fuzzy choice functions revealed preference and rationality abstract this paper investigates the conditions under which a fuzzy set valued choice function is rationalisable by a fuzzy revealed preference relation satisfying certain regularity conditions attention is confined to the case where the domain of the choice function consists of all crisp finite subsets of the universal set of alternatives two sets of weak and strong axioms of fuzzy revealed preference wafrp and safrp are stated in both cases it turns out that wafrp is not equivalent to safrp and that safrp does not characterise rationality in the special case where every set of avialable alternatives has at least one element which is unambiguously chosen wafrp is equivalent to safrp but safrp still does not characterise rationality a fuzzy congruence condition stronger than safrp is proposed and is shown to be necessary and sufficient for rationality

a gauss seidel type solver for the fast computation of input constrained control systems abstract an important class of nonlinear control systems can be represented as the feedback interconnection of two parts a linear time invariant system and a block of decentralized nonlinearities when the linear time invariant part has a nontrivial feedthrough term or the nonlinearity has a feedback gain control computation involves the online implementation of a multivariable algebraic loop which must be resolved at each sampling instant the requirements for such online computation may result in several implementation issues especially in real time and embedded control applications this paper considers the implementation of such algebraic loops arising from several input constrained systems the proposed solution algorithm is globally convergent for a very large class of feedthrough or feedback gains and shows promise for real time and embedded control applications where a fast but approximate solution is of the essence

an interior newton method for quadratic programming quadratic programming represents an extremely important class of optimization problem in this paper we propose a new interior approach for the general quadratic programming problem we establish that our new method is globally and quadratically convergent published alternative interior approaches do not share such strong convergence properties for the nonconvex case we also report on the results of preliminary numerical experiments the results indicate that the proposed method has considerable prcatival potential

merging of bezier curves with box constraints in this paper we present a novel approach to the problem of merging of bezier curves with respect to the l 2 norm we give illustrative examples to show that the solution of the conventional merging problem may not be suitable for further modification and applications as in the case of the degree reduction problem we apply the so called restricted area approach proposed recently in gospodarczyk 2015 to avoid certain defects and make the resulting curve more useful a method of solving the new problem is based on box constrained quadratic programming approach we present a novel approach to the problem of merging of bezier curves we impose constraints of a new type we give illustrative examples to explain the purpose of the new restrictions the merged curve is suitable for further modification and applications

on the regularizing behavior of the sda and sdc gradient methods in the solution of linear ill posed problems we analyze the regularization properties of two recently proposed gradient methods sda and sdc applied to discrete linear inverse problems by studying their filter factors we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution thus yielding a useful filtering effect this behavior is confirmed by numerical experiments performed on some image restoration problems furthermore the experiments show that for severely ill conditioned problems and high noise levels the sda and sdc methods can be competitive with the conjugate gradient cg method since they are slightly slower than cg but exhibit a better semiconvergence behavior

global and asymptotic convergence rate estimates for a class of projected gradient processes projected gradient processes of the goldstein levitin polyak type are considered for constrained minimization problems min omega f with omega a convex set in a hilbert space x and f x to mathbb r 1 a differentiable functional global and local convergence theorems are established for a large class of these processes including those generated with implicit step length rules proposed by bertsekas and goldstein in this analysis traditional uniform strong positivity conditions on the hessian nabla 2 f are replaced by weaker pseudoconvexity conditions and growth conditions on f when f has a unique minimizes in omega convergence rates are shown to depend on how rapidly the function gamma sigma inf r f x f xi mid x in omega x xi geqq sigma grows with increasing sigma 0 if gamma sigma geqq b sigma nu for some b 0 the processes f n in question converge to inf f like o n nu nu 2 linear

a feasible active set method for strictly convex quadratic problems with simple bounds a primal dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of kunisch and rendl siam j optim 14 2003 pp 35 52 based on a guess of the active set a primal dual pair x alpha is computed that satisfies stationarity and the complementary condition if x is not feasible the variables connected to the infeasibilities are added to the active set and a new primal dual pair x alpha is computed this process is iterated until a primal feasible solution is generated then a new active set is determined based on the feasibility information of the dual variable alpha strict convexity of the quadratic problem is sufficient for the algorithm to stop after a finite number of steps with an optimal solution computational experience indicates that this approach also performs well in practice

algorithms for bound constrained quadratic programming problems we present an algorithm which combines standard active set strategies with the gradient projection method for the solution of quadratic programming problems subject to bounds we show in particular that if the quadratic is bounded below on the feasible set then termination occurs at a stationary point in a finite number of iterations moreover if all stationary points are nondegenerate termination occurs at a local minimizer a numerical comparison of the algorithm based on the gradient projection algorithm with a standard active set strategy shows that on mildly degenerate problems the gradient projection algorithm requires considerable less iterations and time than the active set strategy on nondegenerate problems the number of iterations typically decreases by at least a factor of 10 for strongly degenerate problems the performance of the gradient projection algorithm deteriorates but it still performs better than the active set method

an active set newton algorithm for large scale nonlinear programs with box constraints a new algorithm for large scale nonlinear programs with box constraints is introduced the algorithm is based on an efficient identification technique of the active set at the solution and on a nonmonotone stabilization technique it possesses global and superlinear convergence properties under standard assumptions a new technique for generating test problems with known characteristics is also introduced the implementation of the method is described along with computational results for large scale problems

active set support vector regression this paper presents active set support vector regression asvr a new active set strategy to solve a straightforward reformulation of the standard support vector regression problem this new algorithm is based on the successful asvm algorithm for classification problems and consists of solving a finite number of linear equations with a typically large dimensionality equal to the number of points to be approximated however by making use of the sherman morrison woodbury formula a much smaller matrix of the order of the original input space is inverted at each step the algorithm requires no specialized quadratic or linear programming code but merely a linear equation solver which is publicly available asvr is extremely fast produces comparable generalization error to other popular algorithms and is available on the web for download

a solver for nonconvex bound constrained quadratic optimization we present a new algorithm for nonconvex bound constrained quadratic optimization in the strictly convex case our method is equivalent to the state of the art algorithm by dostal and schoberl comput optim appl 30 2005 pp 23 43 unlike their method however we establish a convergence theory for our algorithm that holds even when the problems are nonconvex this is achieved by carefully addressing the challenges associated with directions of negative curvature in particular those that may naturally arise when applying the conjugate gradient algorithm to an indefinite system of equations our presentation and analysis deal explicitly with both lower and upper bounds on the optimization variables whereas the work by dostal and schoberl considers only strictly convex problems with lower bounds to handle this generality we introduce the reduced chopped gradient that is analogous to the reduced free gradient previously used the reduced chopped gradient leads to a new condition that is used to

stochastic stability of nonlinear oscillators the stochastic stability of a nonlinear oscillator parametrically excited by a stationary markov process is considered the stochastic stability problem in terms of a mean first passage time is formulated specifically if the mean first passage time of the energy e of the oscillator to a given energy level is finite then the oscillator is unstable a method of averaging is used to derive a fokker planck equation in the energy variable the stability criterion depends on the nature of the boundary points e 0 and e infty and is expressed in terms of a feller type criterion the stability condition is derived for various types of nonlinearities including coulomb friction in contrast it is observed that the standard stability criterion in terms of lyapunov exponents is inconclusive for this type of problem

a fast algorithm for sparse reconstruction based on shrinkage subspace optimization and continuation we propose a fast algorithm for solving the ell 1 regularized minimization problem min x in mathbb r n mu x 1 ax b 2 2 for recovering sparse solutions to an undetermined system of linear equations ax b the algorithm is divided into two stages that are performed repeatedly in the first stage a first order iterative shrinkage method yields an estimate of the subset of components of x likely to be nonzero in an optimal solution restricting the decision variables x to this subset and fixing their signs at their current values reduces the ell 1 norm x 1 to a linear function of x the resulting subspace problem which involves the minimization of a smaller and smooth quadratic function is solved in the second phase our code fpc as embeds this basic two stage algorithm in a continuation homotopy approach by assigning a decreasing sequence of values to mu this code exhibits state of the art performance in terms of both its speed and its ability to recover sparse signals

acyclic rationality indicators of fuzzy choice functions we introduce the degree of acyclicity of a fuzzy preference relation and two acyclic rationality indicators of a fuzzy choice function c these two indicators measure the degree to which the choice function c is acyclic g rational respectively acyclic m rational we study the fuzzy condorcet property of a fuzzy choice function and the corresponding indicators we express the indicator of g rationality in terms of the condorcet property and the indicator of a consistency

on the structure of fuzzy social welfare functions we investigate the structure of fuzzy aggregation rules which for every permissible profile of individual preferences specify a fuzzy social ordering it is shown that all fuzzy aggregation rules which have non narrow domains and which satisfy the fuzzy counterparts of independence of irrelevant alternatives and pareto criterion are characterized by a distribution of veto power which would be generally considered undesirable

on choosing rationally when preferences are fuzzy abstract in real life exact choices are induced by fuzzy preferences these choices eventually satisfy certain plausible rationality properties several alternative rules for generating exact choices from fuzzy weak preference relations are introduced and the extent to which exact choice sets generated by these rules satisfy fairly weak rationality conditions is studied max min transitivity is shown to be crucial for obtaining a positive result

a further study on rationality conditions of fuzzy choice functions the investigation of rationality plays a central role in the study of fuzzy choice functions in this paper we deal with some important rationality conditions of fuzzy choice functions including weak strong fuzzy congruence axiom weak strong axiom of fuzzy revealed preference fuzzy versions of famous crisp conditions a b c and d etc in the framework of the banerjee choice function we systematically investigate the relationships between these conditions under the assumption that every involved choice set is normal and verify some equivalence results for arbitrary t norms as a result a fuzzy version of the arrow sen theorem is presented the research makes a significant difference compared with the current investigation in the framework of the georgescu choice function

rationality and aggregation of preferences in an ordinally fuzzy framework abstract the paper explores the problem of aggregating ordinally fuzzy individual preferences into ordinally fuzzy social preferences using goguen s ordinal formulation of fuzziness it is shown that given certain plausible conditions the requirement that the society s preferences should satisfy any of several alternative transitivity conditions creates a dilemma either power in the society is rather unevenly distributed or the society tends to be indecisive the problem increases as weaker transitivity conditions are replaced by stronger ones

on the continuous quadratic knapsack problem we introduce a new algorithm for the continuous bounded quadratic knapsack problem this algorithm is motivated by the geometry of the problem is based on the iterative solution of a series of simple projection problems and is easy to understand and implement in practice the method compares favorably to other well known algorithms some of which have superior worst case complexity on problem sizes up ton 4000

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

on the identification of active constraints nondegeneracy conditions that guarantee that the optimal active constraints are identified in a finite number of iterations are studied results of this type have only been established for a few algorithms and then under restrictive hypothesis the main result is a characterization of those algorithms that identify the optimal constraints in a finite number of iterations this result is obtained with a nondegeneracy assumption which is equivalent in the standard nonlinear programming problem to the assumption that there is a set of strictly complementary lagrange multipliers as an important consequence of the authors results the way that this characterization applies to gradient projection and sequential quadratic programming algorithms is shown

the adventures of a simple algorithm abstract this paper presents analyzes and tests a row action method for solving the regularized linear programming problem minimize 1 2 x 2 2 c t x subject to a x b where is a given positive constant the proposed method is based on the observation that the dual of this problem has the form maximize b t y 1 2 a t y c 2 2 subject to y 0 and if y solves the dual then the point x a t y c provides the unique solution of the primal maximizing the dual objective function by changing one variable at a time results in an effective row action method which is suitable for solving large sparse problems one aim of this paper is to clarify the convergence properties of the proposed scheme let y k denote the estimated dual solution at the end of the k th iteration and let x k a t y k c denote the corresponding primal estimate it is proved that the sequence x k converges to x while the sequence y k converges to a point y that solves the dual the only assumption which is needed in order to establish these claims is that the feasible region is not empty yet perhaps the more striking features of the algorithm are related to temporary situations in which it attempts to solve an inconsistent system in such cases the sequence y k obeys the rule y k u k k v where u k is a fastly converging sequence and v is a fixed vector that satisfies a t v 0 and b t v 0 so the sequence x k is almost unchanged for many iterations the paper ends with numerical experiments that illustrate the effects of this phenomenon and the close links with kaczmarz s sor method

an application of fuzzy subsets theory to the analysis of the consumer s spatial preferences abstract this paper discards to usual assumptions of the classical theory of consumer behaviour in mathematical economics first that the consumer is capable of perfectly discriminating between different goods second that the goods capable of satisfying needs are all supplied at a unique point actually consumer behaviour is by nature fuzzy and goods are scattered in a supply space and are transportable in this model the consumer is located at a given point of demand first a general study is made of the structures of spatial preferences in a fuzzy context next the particular properties are introduced in order to define a behaviour of attainable choice then the conditions which guarantee the existence of a completely preordered topological space are imposed in order to verify that the consumer s fuzzy behaviour is coherent these conditions permit to define the existence and continuity of a fuzzy utility as a numerical representation of the imprecise preference the resulting economic theory is neither ordinal nor cardinal but a valuation theory of preference

a direct active set algorithm for large sparse quadratic programs with simple bounds we show how a direct active set method for solving definite and indefinite quadratic programs with simple bounds can be efficiently implemented for large sparse problems all of the necessary factorizations can be carried out in a static data structure that is set up before the numeric computation begins the space required for these factorizations is no larger than that required for a single sparse cholesky factorization of a matrix with the same sparsity structure as the hessian of the quadratic we propose several improvements to this basic algorithm a new way to find a search direction in the indefinite case that allows us to free more than one variable at a time and a new heuristic method for finding a starting point these ideas are motivated by the two norm trust region problem additionally we also show how projection techniques can be used to add several constraints to the active set at each iteration our experimental results show that an algorithm with these improvements runs much faster than the basic algorithm for positive definite problems and finds local minima with lower function values for indefinite problems

bound constrained quadratic programming via piecewise quadratic functions the smallest eigenvalue of a symmetric positive definite matrix and is solved by newton iteration with line search the paper describes the algorithm and its implementation including estimation of 1 how to get a good starting point for the iteration and up and downdating of cholesky factorization results of extensive testing and comparison with other methods for constrained qp are given

projected barzilai borwein methods for large scale box constrained quadratic programming this paper studies projected barzilai borwein pbb methods for large scale box constrained quadratic programming recent work on this method has modified the pbb method by incorporating the grippo lampariello lucidi gll nonmonotone line search so as to enable global convergence to be proved we show by many numerical experiments that the performance of the pbb method deteriorates if the gll line search is used we have therefore considered the question of whether the unmodified method is globally convergent which we show not to be the case by exhibiting a counter example in which the method cycles a new projected gradient method pabb is then considered that alternately uses the two barzilai borwein steplengths we also give an example in which this method may cycle although its practical performance is seen to be superior to the pbb method with the aim of both ensuring global convergence and preserving the good numerical performance of the unmodified methods we examine other recent work on nonmonotone line searches and propose a new adaptive variant with some attractive features further numerical experiments show that the pabb method with the adaptive line search is the best bb like method in the positive definite case and it compares reasonably well against the gpcg algorithm of more and toraldo in the indefinite case the pbb method with the adaptive line search is shown on some examples to find local minima with better solution values and hence may be preferred for this reason

a note on congruence conditions of fuzzy choice functions in order to reflect the fuzziness existing in a choice problem banerjee introduces the concept of fuzzy choice function meanwhile banerjee proposes three congruence conditions in assessing the rationality of a fuzzy choice function in this paper we prove some dependencies among these conditions although banerjee asserts that they are independent

quasi newton updates with bounds we develop a quasi newton method which preserves known bounds on the jacobian matrix we show that this update can be computed with the same amount of work as competitive methods in particular we prove that the number of operations required to obtain this update is proportional to the number of nonzeros in the sparsity pattern of the jacobian matrix the method is also shown to share the local convergence properties of broyden s and schubert s method

on the solution of multidimensional convex separable continuous knapsack problem with bounded variables abstract a minimization problem with a convex separable objective function subject to linear equality constraints and box constraints bounds on the variables is considered necessary and sufficient optimality condition is proved for a feasible solution to be an optimal solution to this problem primal dual analysis is also included examples of some convex separable objective functions for the considered problem are presented

a limited memory quasi newton trust region method for box constrained optimization by means of wolfe conditions strategy we propose a quasi newton trust region method to solve box constrained optimization problems this method is an adequate combination of the compact limited memory bfgs and the trust region direction while the generated point satisfies the wolfe conditions and therefore maintains a positive definite approximation to the hessian of the objective function the global convergence and the quadratic convergence of this method are established under suitable conditions finally we compare our algorithms iwtral and ibwtral with an active set trust region algorithm astral xu and burke 2007 on the cutest box constrained test problems presented by gould et al 2015 numerical results show that the presented method is competitive and totally interesting for solving box constrained optimization