a production transportation problem with stochastic demand and concave production costs the problem of transporting goods from a set of supply points factories to a set of demand points customers so as to minimize linear transportation costs is well known and very efficient solution methods exist in the well known facility location problem one also includes fixed charges for the supply points on the other hand in ordinary transportation problems stochastic demand has been introduced and modelled by convex costs yielding the stochastic transportation problem stp solved by for example the methods in cooper and leblanc 1977 and holmberg and jornsten 1984 however the simultaneous use of these generalizations has recieved little attention until now only a few suggestions for solution methods can be found leblanc 1977 franca and luna 1982 in this paper we consider generalizing this problem even further by introducing general concave costs at the supply points as well as convex costs at the demand points fixed charges are not the only cost structures that occur when producing goods at a factory economies of scale very often yield other concave cost functions

the distribution of maxima of approximately gaussian random fields motivated by the problem of testing for the existence of a signal of known parametric structure and unknown location as explained below against a noisy background we obtain for the maximum of a centered smooth random field an approximation for the tail of the distribution for the motivating class of problems this gives approximately the significance level of the maximum score test the method is based on an application of a likelihood ratio identity followed by approximations of local fields numerical examples illustrate the accuracy of the approximations

an fptas for optimizing a class of low rank functions over a polytope we present a fully polynomial time approximation scheme fptas for optimizing a very general class of non linear functions of low rank over a polytope our approximation scheme relies on constructing an approximate pareto optimal front of the linear functions which constitute the given low rank function in contrast to existing results in the literature our approximation scheme does not require the assumption of quasi concavity on the objective function for the special case of quasi concave function minimization we give an alternative fptas which always returns a solution which is an extreme point of the polytope our technique can also be used to obtain an fptas for combinatorial optimization problems with non linear objective functions for example when the objective is a product of a fixed number of linear functions we also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor unless p np we prove this by showing a similar hardness of approximation result for supermodular function minimization a result that may be of independent interest

some asymptotic results of gaussian random fields with varying mean functions and the associated processes in this paper we derive tail approximations of integrals of exponential functions of gaussian random elds with varying mean functions and approximations of the associated point processes this study is motivated naturally by multiple applications such as hypothesis testing for spatial models study of the distribution of bayesian marginal likelihood and bayes factor and nancial applications

portfolio optimization problem under concave transaction costs and minimal transaction unit constraints we will propose a branch and bound algorithm for calculating a globally optimal solution of a portfolio construction rebalancing problem under concave transaction costs and minimal transaction unit constraints we will employ the absolute deviation of the rate of return of the portfolio as the measure of risk and solve linear programming subproblems by introducing piecewise linear underestimating function for concave transaction cost functions it will be shown by a series of numerical experiments that the algorithm can solve the problem of practical size in an efficient manner

a method for globally minimizing concave functions over convex sets a method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear the algorithm generates linear programs whose solutions minimize the convex envelope of the original function over successively tighter polytopes enclosing the feasible region the algorithm does not involve cuts of the feasible region requires only simplex pivot operations and univariate search computations to be performed allows the objective function to be lower semicontinuous and nonseparable and is guaranteed to converge to the global solution computational aspects of the algorithm are discussed

ramp loss linear programming support vector machine the ramp loss is a robust but non convex loss for classification compared with other non convex losses a local minimum of the ramp loss can be effectively found the effectiveness of local search comes from the piecewise linearity of the ramp loss motivated by the fact that the l1 penalty is piecewise linear as well the l1 penalty is applied for the ramp loss resulting in a ramp loss linear programming support vector machine ramp lpsvm the proposed ramp lpsvm is a piecewise linear minimization problem and the related optimization techniques are applicable moreover the l1 penalty can enhance the sparsity in this paper the corresponding misclassification error and convergence behavior are discussed generally the ramp loss is a truncated hinge loss therefore ramp lpsvm possesses some similar properties as hinge loss svms a local minimization algorithm and a global search strategy are discussed the good optimization capability of the proposed algorithms makes ramp lpsvm perform well in numerical experiments the result of ramp lpsvm is more robust than that of hinge svms and is sparser than that of ramp svm which consists of the k penalty and the ramp loss

real hypersurfaces in the complex quadric with parallel ricci tensor we introduce the notion of parallel ricci tensor for real hypersurfaces in the complex quadric qm som 2 somso2 according to the a principal or the a isotropic unit normal vector field n we give a complete classification of real hypersurfaces in qm som 2 somso2 with parallel ricci tensor

testing for a signal with unknown location and scale in a stationary gaussian random field we suppose that our observations can be decomposed into a fixed signal plus random noise where the noise is modelled as a particular stationary gaussian random field in n dimensional euclidean space the signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude and we are primarily interested in a test to detect such a signal there are many examples where the signal scale or width is assumed known and the test is based on maximising a gaussian random field over all locations in a subset of n dimensional euclidean space the novel feature of this work is that the width of the signal is also unknown and the test is based on maximising a gaussian random field in n 1 dimensions n dimensions for the location plus one dimension for the width two convergent approaches are used to approximate the null distribution one based on the method of knowles and siegmund which uses a version of weyl s tube formula for manifolds with boundaries and the other based on some recent work by worsley which uses the hadwiger characteristic of excursion sets as introduced by adler finally we compare the power of our method with one based on a fixed but perhaps incorrect signal width

real hypersurfaces in complex two plane grassmannians with parallel ricci tensor we introduce the full expression of the curvature tensor of a real hypersurface m in complex two plane grassmannians g 2 m 2 from the gauss equation we then derive a new formula for the ricci tensor of m in g 2 m 2 finally we prove that there does not exist any hopf real hypersurface in complex two plane grassmannians g 2 m 2 with parallel ricci tensor

minimum concave cost production system a further generalization of multi echelon model we will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities the products at some facility are either sent to the next facility or stocked in the warehouse the amount of demand for the final products during periodi i 1 n are known in advance our problem is to minimize the sum of processing holding and backlogging cost all of which are assumed to be concave the origin of this model is the classical economic lot size problem of wagner and whitin and was extensively studied by zangwill this model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems the purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility we will propose an efficient o n4m algorithm for this class of problems

global minimization of a linearly constrained concave function by partition of feasible domain the problem of minimizing a concave function subject to linear inequality constraints may have many local solutions therefore finding the global constrained minimum is a computationally difficult problem a computational method is described which finds the global minimum of a smooth concave function over a polyhedron in rn the feasible domain is partitioned into a rectangular domain which can be excluded from further consideration and r 2n subdomains at least one of which contains the global minimum a known algorithm can be applied sequentially or in parallel to each of these r subdomains to compute the global minimum a method is also presented appendix b for the construction of nontrivial test problems for which the global minimum point is known given an arbitrary polyhedron and a selected vertex it is shown how to determine a concave quadratic function generally with many local minima with its global minimum at the selected vertex

a finite cutting plane method for solving linear programs with an additional reverse convex constraint abstract the paper deals with linear programs with an additional reverse convex constraint if the feasible region of this problem is nonempty and the objective function to be minimized is bounded below on it then the problem has a finite minimum obtained on an at most one dimensional face of the polyhedron as well this paper presents a finite cutting plane method using convexity and disjunctive cuts for solving the considered problem the method is based upon a procedure which for a given nonnegative integer q either finds such an at most q dimensional face of the original polyhedron which has a point feasible to the cuts generated previously or proves that there exists no such a face computational experience is also provided

quasiconjugates of functions duality relationship between quasiconvex minimization under a reverse convex constraint and quasiconvex maximization under a convex constraint and applications abstract in this paper we introduce a concept of quasiconjugate for functions defined on rn whose values are in r the conjugacy correspondence between functions and their quasiconjugates is one to one and symmetric in a class of quasiconvex functions whose minimizer on rn is located at the origin by using the concept of quasiconjugate we obtain a duality relationship between quasiconvex minimization under a reverse convex constraint and quasiconvex maximization under a convex constraint this duality relationship allows us to establish a primal dual pair in a class of nonconvex optimization problems without the duality gap several applications are given

some relations between dualities polarities coupling functionals and conjugations on etablit certaines relations entre dualites au sens de evers et van maaren 1981 polarites comme celles utilisees dans griffin araoz et edmonds 1982 fonctionnelles de couplage au sens de moreau 1966 1967 1970 et conjugaisons comme celles introduites par l auteur 1983

tilted euler characteristic densities for central limit random fields with application to bubbles local increases in the mean of a random field are detected con servatively by thresholding a field of test statistics at a level u chosen to control the tail probability or p value of its maximum this p value is approximated by the expected euler characteristic ec of the ex cursion set of the test statistic field above u denoted e au under isotropy one can use the expansion e au p k vkk u where vk is an intrinsic volume of the parameter space andk is an ec density of the field ec densities are available for a number of pro cesses mainly those constructed from multivariate gaussian fields via smooth functions using saddlepoint methods we derive an ex pansion fork u for fields which are only approximately gaussian but for which higher order cumulants are available we focus on linear combinations of n independent non gaussian fields whence a central limit theorem is in force the threshold u is allowed to grow with the sample size n in which case our expression has a smaller relative asymptotic error than the gaussian ec density several illustrative examples including an application to bubbles data accompany the theory

a combined cutting stock and lot sizing problem abstract a combined cutting stock and lot sizing problem with a joint setup cost is formulated under static and deterministic conditions reducing this problem by disregarding the joint setup cost and integer lot sizes results in a non linear minimization problem with a concave objective function and linear constraints solution procedures for this type of optimization problem are considered and some specialized heuristics are suggested numerical examples to indicate the performances of the procedures are also presented

cutting planes for low rank like concave minimization problems concavity cuts play an important role in several algorithms for concave minimization such as pure cutting plane algorithms conical algorithms and branch and bound algorithms for concave quadratic minimization problems konno et al 1998 have demonstrated that the lower the rank of the problem i e the smaller the number of nonlinear variables the deeper the concavity cuts usually turn out to be in this paper we examine the case where the number of nonlinear variables of a concave minimization problem is large but most of the objective value of a good solution is determined by a small number of variables only we will discuss ways to exploit such a situation to derive deep cutting planes to this end we apply concepts usually applied for efficiently solving low rank concave minimization problems

rotation space random fields with an application to fmri data siegmund and worsley considered the problem of testing for a signal with unknown location and scale in a gaussian random field defined on r n the test statistic was the maximum of a gaussian random field in an n 1 dimensional scale space n dimensions for location and one dimension for the scale of a smoothing kernel siegmund and worsley used two methods one involving the expected euler characteristic of the excursion set and the other involving the volume of tubes to derive an approximate null distribution the purpose of this paper is to extend the scale space result to the rotation space random field when n 2 where the maximum is taken over all rotations of the filter as well as scales we apply this result to the problem of searching for activation in brain images obtained by functional magnetic resonance imaging fmri

linear multiplicative programming an algorithm for solving a linear multiplicative programming problem referred to as lmp is proposed lmp minimizes the product of two linear functions subject to general linear constraints the product of two linear functions is a typical non convex function so that it can have multiple local minima it is shown however that lmp can be solved efficiently by the combination of the parametric simplex method and any standard convex minimization procedure the computational results indicate that the amount of computation is not much different from that of solving linear programs of the same size in addition the method proposed for lmp can be extended to a convex multiplicative programming problem cmp which minimizes the product of two convex functions under convex constraints