realizing rotation vectors for torus homeomorphisms we consider the rotation set p f for a lift f of a homeomorphism f t2 t2 which is homotopic to the identity our main result is that if a vector v lies in the interior of p f and has both coordinates rational then there is a periodic point x e t2 with the property that

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

internal diffusion limited aggregation parallel algorithms and complexity the computational complexity of internal diffusion limited aggregation dla is examined from both a theoretical and a practical point of view we show that for two or more dimensions the problem of predicting the cluster from a given set of paths is complete for the complexity class cc the subset of p characterized by circuits composed of comparator gates cc completeness is believed to imply that in the worst case growing a cluster of size n requires polynomial time in n even on a parallel computer a parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths and then corrects defects in the guessed cluster through a nonlocal annihilation process the parallel running time of the relaxation algorithm for two dimensional internal dla is studied by simulating it on a serial computer the numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n thus the computational resources needed to grow large clusters are significantly less on average than the worst case analysis would suggest for a parallel machine with k processors we show that random clusters in d dimensions can be generated in mathcal o n k logk n 2 d steps this is a significant speedup over explicit sequential simulation which takes mathcal o n 1 2 d time on average finally we show that in one dimension internal dla can be predicted in mathcal o logn parallel time and so is in the complexity class nc

limiting shapes for deterministic centrally seeded growth models we study the rotor router model and two deterministic sandpile models for the rotor router model in z d levine and peres proved that the limiting shape of the growth clus ter is a sphere for the other two models only bounds in dimension 2 are known a unified approach for these models with a new parameter h the initial number of particles at each site allows to prove a number of new limiting shape results in any dimension d 1 for the rotor router model the limiting shape is a sphere for all values of h for one of the sandpile models and h 2d 2 the maximal value the limiting shape is a cube for both sandpile models the limiting shape is a sphere in the limit h finally we prove that the rotor router shape contains a diamond

adaptive kernel search a heuristic for solving mixed integer linear programs abstract we introduce adaptive kernel search aks a heuristic framework for the solution of general mixed integer linear programs mips aks extends and enhances kernel search a heuristic framework that has been shown to produce high quality solutions for a number of specific combinatorial optimization problems in a short amount of time aks solves a sequence of carefully constructed restricted mips using a commercial mip solver the computational effort required to solve the first restricted mip guides the construction of the subsequent mips the restricted mips are constructed around a kernel which contains the variables that are presumably non zero in an optimal solution computational results for a set of 137 instances show that aks significantly outperforms other state of the art heuristics for solving mips aks also compares favorably to cplex and offers more flexibility to trade off solution quality and computing time

a new class of functions for measuring solution integrality in the feasibility pump approach mixed integer optimization is a powerful tool for modeling many optimization problems arising from real world applications finding a first feasible solution represents the first step for several mixed integer programming mip solvers the feasibility pump is a heuristic for finding feasible solutions to mixed integer linear programming milp problems which is effective even when dealing with hard mip instances in this work we start by interpreting the feasibility pump as a frank wolfe method applied to a nonsmooth concave merit function then we define a general class of functions that can be included in the feasibility pump scheme for measuring solution integrality and we identify some merit functions belonging to this class we further extend our approach by dynamically combining two different merit functions finally we define a new version of the feasibility pump algorithm which includes the original version of the feasibility pump as a special case and we present computational results on bi

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

a feasibility pump for mixed integer nonlinear programs we present an algorithm for finding a feasible solution to a convex mixed integer nonlinear program this algorithm called feasibility pump alternates between solving nonlinear programs and mixed integer linear programs we also discuss how the algorithm can be iterated so as to improve the first solution it finds as well as its integration within an outer approximation scheme we report computational results

on an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems in this paper we study a new exact and smooth penalty function for the nonlinear mixed discrete programming problem by augumenting only one variable no matter how many constraints through the smooth and exact penalty function we can transform the nonlinear mixed discrete programming problem into an unconstrained optimization model we demonstrate that under mild conditions when the penalty parameter is sufficiently large optimizers of this penalty function are precisely the optimizers of the nonlinear mixed discrete programming problem alternatively under some mild assumptions the local exactness property is also presented the numerical results demonstrate that the new penalty function is an effective and promising approach as important applications we solve an increasingly popular search engine advertising problem via the new proposed penalty function

periodic approximations of irrational pseudo rotations using pseudoholomorphic curves we prove that every c 1 smooth area preserving dieomorphism of the closed 2 disk having not more than one periodic point is the uniform limit of periodic c 1 smooth dieomorphisms in particular every smooth irrational pseudo rotation can be c 0 approximated by integrable systems this partially answers a long standing question of a katok regarding zero entropy hamiltonian systems in low dimensions our approach uses pseudoholomorphic curve techniques from symplectic geometry

octane a new heuristic for pure 0 1 programs we propose a new heuristic for pure 0 1 programs which finds feasible integer points by enumerating extended facets of the octahedron the outer polar of the unit hypercube we give efficient algorithms to carry out the enumeration and we explain how our heuristic can be embedded in a branch and cut framework finally we present computational results on a set of pure 0 1 programs taken from miplib and other sources

solving zero one mixed integer programming problems using tabu search we describe a tabu search ts approach for solving general zero one mixed integer programming mip problems that exploits the extreme point property of zero one solutions specialized choice rules and aspiration criteria are identified for the problems expressed as functions of integer infeasibility measures and objective function values the first level ts mechanisms are then extended with advanced level strategies and learning we also look at probabilistic measures in this framework and examine how the learning tool target analysis ta can be applied to identify better control structures and decision rules computational results are reported on a portfolio of multiconstraint knapsack problems our approach is designed to solve thoroughly general 0 1 mip problems and thus contains no problem domain specific knowledge yet it obtains solutions for the multiconstraint knapsack problem whose quality rivals and in some cases surpasses the best solutions obtained by special purpose methods that have been created to exploit the special structure of these problems

ensembles invariants non enlaces des diffeomorphismes du tore et de l anneau we introduce the notion of unlinked invariant set for a diffeomorphism of the 2 torus or the closed annulus and we look at the properties of these sets which generalize the aubry mather sets we prove that for any irrational number in the rotation set of an area preserving diffeomorphism of the annulus there exists an unliked invariant set whose rotation set is reduced to in the same way we prove that any minimal diffeomorphism of the 2 torus homotopic to the identity may be approximated in the c 0 topology by a periodic diffeomorphism

a storm of feasibility pumps for nonconvex minlp one of the foremost difficulties in solving mixed integer nonlinear programs either with exact or heuristic methods is to find a feasible point we address this issue with a new feasibility pump algorithm tailored for nonconvex mixed integer nonlinear programs feasibility pumps are algorithms that iterate between solving a continuous relaxation and a mixed integer relaxation of the original problems such approaches currently exist in the literature for mixed integer linear programs and convex mixed integer nonlinear programs both cases exhibit the distinctive property that the continuous relaxation can be solved in polynomial time in nonconvex mixed integer nonlinear programming such a property does not hold and therefore special care has to be exercised in order to allow feasibility pump algorithms to rely only on local optima of the continuous relaxation based on a new high level view of feasibility pump algorithms as a special case of the well known successive projection method we show that many possible different variants of the approach can be developed depending on how several different orthogonal implementation choices are taken a remarkable twist of feasibility pump algorithms is that unlike most previous successive projection methods from the literature projection is naturally taken in two different norms in the two different subproblems to cope with this issue while retaining the local convergence properties of standard successive projection methods we propose the introduction of appropriate norm constraints in the subproblems these actually seem to significantly improve the practical performance of the approach we present extensive computational results on the minlplib showing the effectiveness and efficiency of our algorithm

realizing rotation numbers on annular continua an annular continuum is a compact connected set k which separates a closed annulus a into exactly two connected components one containing each boundary component the topology of such continua can be very intricate for instance non locally connected we adapt a result proved by handel in the case where k a showing that if k is an invariant annular continuum of a homeomorphism of a isotopic to the identity then the rotation set in k is closed moreover every element of the rotation set is realized by an ergodic measure supported in k and by a periodic orbit if the rotation number is rational and most elements are realized by a compact invariant set our second result shows that if the continuum k is minimal with the property of being annular what we call a circloid then every rational number between the extrema of the rotation set in k is realized by a periodic orbit in k as a consequence the rotation set is a closed interval and every number in this interval rational or not is realized by an orbit moreover by an ergodic measure in k this improves a previous result of barge and gillette

logarithmic fluctuations for internal dla let each of n particles starting at the origin in z 2 perform simple random walk until reaching a site with no other particles lawler bramson and griffeath proved that the resulting random set a n of n occupied sites is with high probability close to a disk br of radius r p n we show that the discrepancy between a n and the disk is at most logarithmic in the radius i e there is an absolute constant c such that with probability 1 br c log r a r 2 br c log r for all suciently large r

solving multiobjective mixed integer convex optimization problems multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the varia

the rotation set of a homeomorphism of the annulus is closed we show that the rotation set for any orientation preserving boundary component preserving homeomorphism of the annulus is closed in particular if the homeomorphism is area preserving then the rotation set is a closed interval

internal dla and the stefan problem generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as poisson sources of particles which then perform symmetric random walks with an attractive zero range interaction until they reach the first site which has been visited by fewer than alpha particles at which point they stop sites on which particles are frozen constitute the occupied set we prove that in appropriate regimes the particle density has a hydrodynamic limit which is the one phase stefan problem this is then used to study the asymptotic behavior of the occupied set in two dimensions when the walks are independent with one source at the origin and alpha 1 we obtain in particular that the occupied set is asymptotically a disc of radius k sqrt t where k is the solution of exp k 2 4 pi k 2 settling a conjecture of lawler bramson and griffeath

exploring relaxation induced neighborhoods to improve mip solutions given a feasible solution to a mixed integer programming mip model a natural question is whether that solution can be improved using local search techniques local search has been applied very successfully in a variety of other combinatorial optimization domains unfortunately local search relies extensively on the notion of a solution neighborhood and this neighborhood is almost always tailored to the structure of the particular problem being solved a mip model typically conveys little information about the underlying problem structure this paper considers two new approaches to exploring interesting domain independent neighborhoods in mip the more effective of the two which we call relaxation induced neighborhood search rins constructs a promising neighborhood using information contained in the continuous relaxation of the mip model neighborhood exploration is then formulated as a mip model itself and solved recursively the second which we call guided dives is a simple modification of the mip tree traversal order loosely speaking it guides the search towards nodes that are close neighbors of the best known feasible solution extensive computational experiments on very difficult mip models show that both approaches outperform default cplex mip and a previously described approach for exploring mip neighborhoods local branching with respect to several different metrics the metrics we consider are quality of the best integer solution produced within a time limit ability to improve a given integer solution of both good and poor quality and time required to diversify the search in order to find a new solution

subdiffusive fluctuations for internal diffusion limited aggregation internal diffusion limited aggregation internal dla is a cluster model in z d where new points are added by starting random walkers at the origin and letting them run until they have found a new point to add to the cluster it has been shown that the limiting shape of internal dla clusters is spherical here we show that for d 2 the fluctuations are subdiffusive in fact that they are of order at most n 1 3 at least up to logarithmic corrections more precisely we show that for all sufficiently large n the cluster after m d n d steps covers all points in the ball of radius n n 1 3 in n 2 and is contained in the ball of radius n n 1 3 in n 4

the feasibility pump in this paper we consider the np hard problem of finding a feasible solution if any exists for a generic mip problem of the form min ctx ax b xj integer j trivially a feasible solution can be defined as a point x p x ax b that is equal to its rounding where the rounded point is defined by x j if j and x j otherwise and represents scalar rounding to the nearest integer replacing equal with as close as possible relative to a suitable distance function x suggests the following feasibility pump fp heuristic for finding a feasible solution of a given mip we start from any x p and define its rounding at each fp iteration we look for a point x p that is as close as possible to the current by solving the problem min x x p assuming x is chosen appropriately this is an easily solvable lp problem if x 0 then x is a feasible mip solution and we are done otherwise we replace by the rounding of x and repeat we report computational results on a set of 83 difficult 0 1 mips using the commercial software ilog cplex 8 1 as a benchmark the outcome is that fp in spite of its simple foundation proves competitive with ilog cplex both in terms of speed and quality of the first solution delivered interestingly ilog cplex could not find any feasible solution at the root node for 19 problems in our test bed whereas fp was unsuccessful in just 3 cases

a heuristic ceiling point algorithm for general integer linear programming this paper first examines the role of ceiling points in solving a pure general integer linear programming problem p several kinds of ceiling points are defined and analyzed and one kind called feasible 1 ceiling points proves to be of special interest we demonstrate that all optimal solutions for a problem p whose feasible region is nonempty and bounded are feasible 1 ceiling points consequently such a problem may be solved by enumerating just its feasible 1 ceiling points the paper then describes an algorithm called the heuristic ceiling point algorithm hcpa which approximately solves p by searching only for feasible 1 ceiling points relatively near the optimal solution for the lp relaxation such solutions are apt to have a high possibly even optimal objective function value the results of applying the hcpa to 48 test problems taken from the literature indicate that this approach usually yields a very good solution with a moderate amount of computational effort