a computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set the separable uncertainty sets have been widely used in robust portfolio selection models e g see erdogan et al robust portfolio management manuscript department of industrial engineering and operations research columbia university new york 2004 goldfarb and iyengar math oper res 28 1 38 2003 tutuncu and koenig ann oper res 132 157 187 2004 for these uncertainty sets each type of uncertain parameters e g mean and covariance has its own uncertainty set as addressed in lu a new cone programming approach for robust portfolio selection technical report department of mathematics simon fraser university burnaby 2006 robust portfolio selection based on a joint ellipsoidal uncertainty set manuscript department of mathematics simon fraser university burnaby 2008 these separable uncertainty sets typically share two common properties i their actual confidence level namely the probability of uncertain parameters falling within the uncertainty set is unknown and it can be much higher than the desired one and ii they are fully or partially box type the associated consequences are that the resulting robust portfolios can be too conservative and moreover they are usually highly non diversified as observed in the computational experiments conducted in this paper and tutuncu and koenig ann oper res 132 157 187 2004 to combat these drawbacks the author of this paper introduced a joint ellipsoidal uncertainty set lu in a new cone programming approach for robust portfolio selection technical report department of mathematics simon fraser university burnaby 2006 robust portfolio selection based on a joint ellipsoidal uncertainty set manuscript department of mathematics simon fraser university burnaby 2008 and showed that it can be constructed as a confidence region associated with a statistical procedure applied to estimate the model parameters for this uncertainty set we showed in lu a new cone programming approach for robust portfolio selection technical report department of mathematics simon fraser university burnaby 2006 robust portfolio selection based on a joint ellipsoidal uncertainty set manuscript department of mathematics simon fraser university burnaby 2008 that the corresponding robust maximum risk adjusted return rmrar model can be reformulated and solved as a cone programming problem in this paper we conduct computational experiments to compare the performance of the robust portfolios determined by the rmrar models with our joint uncertainty set lu in a new cone programming approach for robust portfolio selection technical report department of mathematics simon fraser university burnaby 2006 robust portfolio selection based on a joint ellipsoidal uncertainty set manuscript department of mathematics simon fraser university burnaby 2008 and goldfarb and iyengar s separable uncertainty set proposed in the seminal paper goldfarb and iyengar in math oper res 28 1 38 2003 our computational results demonstrate that our robust portfolio outperforms goldfarb and iyengar s in terms of wealth growth rate and transaction cost and moreover ours is fairly diversified but goldfarb and iyengar s is surprisingly highly non diversified

robust novelty detection via worst case cvar minimization novelty detection models aim to find the minimum volume set covering a given probability mass this paper proposes a robust single class support vector machine ssvm for novelty detection which is mainly based on the worst case conditional value at risk minimization by assuming that every input is subject to an uncertainty with a specified symmetric support this robust formulation results in a maximization term that is similar to the regularization term in the classical ssvm when the uncertainty set is ell 1 norm ell infty norm or box its training can be reformulated to a linear program while the uncertainty set is ell 2 norm or ellipsoidal its training is a tractable second order cone program the proposed method has a nice consistent statistical property as the training size goes to infinity the estimated normal region converges to the true provided that the magnitude of the uncertainty set decreases in a systematic way the experimental results on three data sets clearly demonstrate its superiority over three benchmark models

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

a digit by digit algorithm for mth root extraction a general digit recurrence algorithm for the computation of the mth root with an m integer is presented in this paper based on the concept of completing the mth root a detailed analysis of the convergence conditions is performed and iteration independent digit selection rules are obtained for any radix and redundant digit set a radix 2 version for mth rooting is also studied together with closed formulas for both the digit selection rules and the number of bits required to perform correct selections

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

worst case robust omega ratio abstract the omega ratio is a recent performance measure proposed to overcome the known shortcomings of the sharpe ratio until recently the omega ratio was thought to be computationally intractable and research was focused on heuristic optimization procedures we have shown elsewhere that the omega ratio optimization is equivalent to a linear program and hence can be solved exactly in polynomial time this permits the investigation of more complex and realistic variants of the problem the standard formulation of the omega ratio requires perfect information for the probability distribution of the asset returns in this paper we investigate the problem arising from the probability distribution of the asset returns being only partially known we introduce the robust variant of the conventional omega ratio that hedges against uncertainty in the probability distribution we examine the worst case omega ratio optimization problem under three types of uncertainty mixture distribution box and ellipsoidal uncertainty and show that the problem remains tractable

robust portfolio selection problems in this paper we show how to formulate and solve robust portfolio selection problems the objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters we introduce uncertainty structures for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second order cone programs and therefore the computational effort required to solve them is comparable to that required for solving convex quadratic programs moreover we show that these uncertainty structures correspond to confidence regions associated with the statistical procedures employed to estimate the market parameters finally we demonstrate a simple recipe for efficiently computing robust portfolios given raw market data and a desired level of confidence

a probabilistic model for minmax regret in combinatorial optimization in this paper we propose a new probabilistic model for minimizing the anticipated regret in combinatorial optimization problems with distributional uncertainty in the objective coefficients the interval uncertainty representation of data is supplemented with information on the marginal distributions as a decision criterion we minimize the worst case conditional value at risk of regret the proposed model includes the interval data minmax regret model as a special case for the class of combinatorial optimization problems with a compact convex hull representation a polynomial sized mixed integer linear program is formulated when a the range and mean are known and b the range mean and mean absolute deviation are known and a mixed integer second order cone program is formulated when c the range mean and standard deviation are known for the subset selection problem of choosing k elements of maximum total weight out of a set of n elements the probabilistic regret model is shown to be solvable in polynomial time in the instances a and b above this extends the current known polynomial complexity result for minmax regret subset selection with range information only

fast delaunay triangulation in three dimensions abstract an efficient algorithm for delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process new features include the search of a neighbouring point by the layering scheme locating the containing tetrahedron by random walk formulas of important geometrical quantities of a new tetrahedron based on those of an existing one a novel approach in establishing the adjacency relationship the use of adjacency table and the management of memory the resulting scheme is one of the fastest triangulation algorithms known to the authors which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a hp 735 machine

credit risk optimization with conditional value at risk criterion this paper examines a new approach for credit risk optimization the model is based on the conditional value at risk cvar risk measure the expected loss exceeding value at risk cvar is also known as mean excess mean shortfall or tail var this model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize cvar subject to trading and return constraints the credit risk distribution is generated by monte carlo simulations and the optimization problem is solved effectively by linear programming the algorithm is very efficient it can handle hundreds of instruments and thousands of scenarios in reasonable computer time the approach is demonstrated with a portfolio of emerging market bonds

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

qualitative measures for initial meshes this paper reviews geometric measures used to assess the shape of finite elements in two and three dimensional meshes measures have been normalized and made scale invariant whenever possible this paper also introduces a universal similarity region that enhances comparisons of triangles and their measures as a byproduct the usr provides a dynamic way to compare improved triangular meshes copyright 2000 john wiley sons ltd

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

adaptive finite element methods for elliptic pdes based on conforming centroidal voronoi delaunay triangulations a new triangular mesh adaptivity algorithm for elliptic pdes that combines a posteriori error estimation with centroidal voronoi delaunay tessellations of domains in two dimensions is proposed and tested the ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features including the following errors are very well equidistributed over the triangles at all levels of refinement the triangles remain very well shaped even if the grid size at any particular refinement level when viewed globally varies by several orders of magnitude and the convergence rates achieved are the best obtainable using piecewise linear finite elements this methodology can be easily extended to higher order finite element approximations or mixed finite element formulations although only the linear approximation is considered in this paper

radix 4 reciprocal square root and its combination with division and square root in this work we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix 4 implementation as in similar algorithms for division and square root the results are obtained correctly rounded in a straightforward manner in contrast to existing methods to compute the reciprocal square root although apparently a single selection function can only be used for j spl ges 2 the selection constants are different for j 0 j 1 and j spl ges 2 we show that it is possible to use a single selection function for all iterations we perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency especially for exactly rounded results we also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit

delaunay triangulation in computational fluid dynamics abstract a method which utilises the delaunay criterion is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed an algorithm is briefly outlined to construct the triangulation and its dual the voronoi diagram issues related to how to construct boundary conforming grids from such a triangulation are addressed and details are presented of how grid points within the domain can be generated automatically the point generation algorithm utilises either the given boundary point distribution or for grid adaption a background mesh computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered examples of meshes and flow computations for a range of aerospace geometries are presented

grid generation and optimization based on centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding voronoi regions such tessellations are of use in very diverse applications including data compression clustering analysis cell biology territorial behavior of animals and optimal allocation of resources in this paper we explore the use of cvts in grid generation in connection with finite element approximations of partial differential equations we being by describing these tessellations and methods for their determination we then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations

convergence of the lloyd algorithm for computing centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids mass centers of the corresponding voronoi regions with respect to a given density function centroidal voronoi tessellations may also be defined in more abstract and more general settings due to the natural optimization properties enjoyed by cvts they have many applications in diverse fields the lloyd algorithm is one of the most popular iterative schemes for computing the cvts but its theoretical analysis is far from complete in this paper some new analytical results on the local and global convergence of the lloyd algorithm are presented these results are derived through careful utilization of the optimization properties shared by cvts numerical experiments are also provided to substantiate the theoretical analysis

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

robust optimization methodology and applications robust optimization ro is a modeling methodology combined with computational tools to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set the paper surveys the main results of ro as applied to uncertain linear conic quadratic and semidefinite programming for these cases computationally tractable robust counterparts of uncertain problems are explicitly obtained or good approximations of these counterparts are proposed making ro a useful tool for real world applications we discuss some of these applications specifically antenna design truss topology design and stability analysis synthesis in uncertain dynamic systems we also describe a case study of 90 lps from the netlib collection the study reveals that the feasibility properties of the usual solutions of real world lps can be severely affected by small perturbations of the data and that the ro methodology can be successfully used to overcome this phenomenon

worst case conditional value at risk with application to robust portfolio management this paper considers the worst case conditional value at risk cvar in the situation where only partial information on the underlying probability distribution is available the minimization of the worst case cvar under mixture distribution uncertainty box uncertainty and ellipsoidal uncertainty are investigated the application of the worst case cvar to robust portfolio optimization is proposed and the corresponding problems are cast as linear programs and second order cone programs that can be solved efficiently market data simulation and monte carlo simulation examples are presented to illustrate the proposed approach

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

generating scenario trees for multistage decision problems in models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models if the uncertainties are expressed in terms of multivariate continuous distributions or a discrete distribution with far too many outcomes we normally face two possibilities either creating a decision model with internal sampling or trying to find a simple discrete approximation of the given distribution that serves as input to the model this paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties users are free to specify any statistical properties they find relevant and the method can handle inconsistencies in the specifications the basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties we illustrate the method by single and multiple period problems the results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications we discuss how to verify that the relevant statistical properties are captured in these specifications and argue that what are the relevant properties will be problem dependent

fast centroidal voronoi delaunay triangulation for unstructured mesh generation a fast unstructured mesh generation algorithm based on conforming centroidal voronoi delaunay triangulation cfcvdt algorithm ju 2007 is proposed in this paper in the new algorithm the constrained delaunay triangulation cdt algorithm is used only for the generation of the initial mesh the mesh quality shall be continuously improved by updating the positions of vertices and flipping edges in a number of iterations since the most time consuming procedure in cfcvdt algorithm is the cdt in each iteration which has been successfully avoided in this new algorithm the efficiency has been significantly improved furthermore the meshes generated by this algorithm have similar high quality features as that generated by cfcvdt when complex interfaces are involved our algorithm can keep the mesh conforming to the interfaces very efficiently by using various density functions this algorithm can produce high quality non uniform meshes for potentially many applications a fast high quality triangular mesh generation algorithm fcfcvdt is proposed based on the cfcvdt algorithm the fcfcvdt algorithm significantly improves the efficiency of cfcvdt algorithm at the same time maintains the mesh quality it is capable of generating high quality body interface fitted meshes for complicate domains interfaces

distributionally robust control of constrained stochastic systems we investigate the control of constrained stochastic linear systems when faced with limited information regarding the disturbance process i e when only the first two moments of the disturbance distribution are known we consider two types of distributionally robust constraints in the first case we require that the constraints hold with a given probability for all disturbance distributions sharing the known moments these constraints are commonly referred to as distributionally robust chance constraints in the second case we impose conditional value at risk cvar constraints to bound the expected constraint violation for all disturbance distributions consistent with the given moment information such constraints are referred to as distributionally robust cvar constraints with second order moment specifications we propose a method for designing linear controllers for systems with such constraints that is both computationally tractable and practically meaningful for both finite and infinite horizon problems we prove in the infinite horizon case that our design procedure produces the globally optimal linear output feedback controller for distributionally robust cvar and chance constrained problems the proposed methods are illustrated for a wind blade control design case study for which distributionally robust constraints constitute sensible design objectives

constructing risk measures from uncertainty sets we illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance and show how robust optimization can be used to generalize the concepts of these risk measures we also show that by using properly defined uncertainty sets in robust optimization models one can construct coherent risk measures and address the issue of the computational tractability of the resulting formulations our results have implications for efficient portfolio optimization under different measures of risk

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments