clarke coderivatives of efficient point multifunctions in parametric vector optimization abstract the paper is devoted to the study of the clarke circatangent coderivatives of the efficient point multifunction of parametric vector optimization problems in banach spaces we provide inner outer estimates for evaluating the clarke circatangent coderivative of this multifunction in a broad class of conventional vector optimization problems in the presence of geometrical operator and finite and infinite functional constraints examples are given for analyzing and illustrating the obtained results

the continuum random tree iii let mathscr r k k geq 1 be random trees with k leaves satisfying a consistency condition removing a random leaf from mathscr r k gives mathscr r k 1 then under an extra condition this family determines a random continuum tree mathscr l which it is convenient to represent as a random subset of l 1 this leads to an abstract notion of convergence in distribution as n rightarrow infty of rescaled random trees mathscr j n on n vertices to a limit continuum random tree mathscr l the notion is based upon the assumption that for fixed k the subtrees of mathscr j n determined by k randomly chosen vertices converge to mathscr r k as our main example under mild conditions on the offspring distribution the family tree of a galton watson branching process conditioned on total population size equal to n can be rescaled to converge to a limit continuum random tree which can be constructed from brownian excursion

necessary conditions for constrained optimization problems with semicontinuous and continuous data we consider nonsmooth constrained optimization problems with semicontinuous and continuous data in banach space and derive necessary conditions sl without constraint qualification in terms of smooth subderivatives and normal cones these results in different versions are set in reflexive and smooth banach spaces

a biological algorithm to solve the assignment problem based on dna molecules computation abstract the assignment problem ap is to optimally solve the task of assigning n jobs to n individuals such that minimum cost or maximum profit can be obtained it is a vitally important np complete problem in operation management and applied mathematics having a wide range of applications in this paper we present a new parallel dna algorithm to solve the assignment problem using dna molecular operations meanwhile we design flexible length dna strands to represent different jobs and individuals take appropriate steps and get the solutions of the ap in proper length range and with o n 2 time complexity we extend the application of dna molecular operations and simultaneity reduce the complexity of the computation

optimality conditions for henig and globally proper efficient solutions with ordering cone has empty interior in this paper we consider the set valued vector optimization problems with constraint in locally convex spaces we present the necessary and sufficient conditions for henig efficient solution pair globally proper efficient solution pair and super efficient solution pair without the ordering cones having the nonempty interior

the lagrange multiplier rule for multifunctions in banach spaces we study general constrained multiobjective optimization problems with objectives being closed multifunctions in banach spaces in terms of the coderivatives and normal cones we provide generalized lagrange multiplier rules as necessary optimality conditions of the above problems in an asplund space setting sharper results are presented

the fermat rule for multifunctions on banach spaces using variational analysis we study vector optimization problems with objectives being closed multifunctions on banach spaces or in asplund spaces in particular in terms of the coderivatives we present fermat s rules as necessary conditions for an optimal solution of the above problems as applications we also provide some necessary conditions in terms of clarke s normal cones or the limiting normal cones for pareto efficient points

the lagrange multiplier rule in set valued optimization the known lagrange multiplier rule is extended to set valued constrained optimization problems using the contingent epiderivative as differentiability notion a necessary optimality condition for weak minimizers is derived which is also a sufficient condition under generalized convexity assumptions

solving the minimum bisection problem using a biologically inspired computational model the traditional trend of dna computing aims at solving computationally intractable problems the minimum bisection problem mbp is a well known np hard problem which is intended to partition the vertices of a given graph into two equal halves so as to minimize the number of those edges with exactly one end in each half based on a biologically inspired computational model this paper describes a novel algorithm for the minimum bisection problem which requires a time cost and a dna strand length that are linearly proportional to the instance size

the fermat rule for multifunctions for super efficiency abstract using variational analysis we study the vector optimization problems with objectives being closed multifunctions on banach spaces or in asplund spaces in terms of the coderivatives and normal cones we present fermat s rules as necessary or sufficient conditions for a super efficient solution of the above problems

scalar multiplier rules in set valued optimization in this work we establish necessary and sufficient conditions for weak minimizers of a constrained set valued optimization problem these conditions are given by means of multiplier rules formulated in terms of contingent epiderivatives of scalar set valued maps we consider that the image spaces are finite dimensional and the set valued maps are convex and stable for these conditions our results provide a scalar version of analogous existing results in the literature under weaker existence conditions moreover we prove that the multiplier rules can be computed in terms of the directional derivative of associated maps of infima

super efficiency in vector optimization we introduce a new concept of efficiency in vector optimization this concept super efficiency is shown to have many desirable properties in particular we show that in reasonable settings the super efficient points of a set are norm dense in the efficient frontier we also provide a chebyshev characterization of super efficient points for nonconvex sets and a scalarization theory when the underlying set is convex

exit times for an increasing levy tree valued process we give an explicit construction of the increasing tree valued process introduced by abraham and delmas using a random point process of trees and a grafting procedure this random point process will be used in companion papers to study record processes on levy trees we use the poissonian structure of the jumps of the increasing tree valued process to describe its behavior at the first time the tree grows higher than a given height using a spinal decomposition of the tree similar to the classical bismut and williams decompositions we also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree valued process

branching processes in levy processes laplace functionals of snakes and superprocesses we use the exploration process introduced in a previous work to develop a new construction of superprocesses with a general branching mechanism this construction depends on a path valued process called the levy snake which is of independent interest our method of proof involves a calculation of the laplace functional of the occupation field of the levy snake this calculation relies on an evaluation of the corresponding moment functionals which requires precise information about the underlying genealogical structure

solving traveling salesman problem in the adleman lipton model abstract the traveling salesman problem is to find a minimum cost weight path for a given set of cities vertices and roads edges the path must start at a specified city and end there after going through all the other given cites only once it is a classical np complete problem in graph theory in this paper we consider a dna procedure for solving the traveling salesman problem in the adleman lipton model the procedure works in o n steps for the traveling salesman of an edge weighted graph with n vertices

super efficiency of vector optimization in banach spaces using variational analysis in terms of the clarke normal cone we consider super efficiency of vector optimization in banach spaces we establish some characterizations for super efficiency in particular dropping the assumption that the ordering cone has a bounded base we extend a result in borwein and zhuang j m borwein d zhuang super efficiency in vector optimization trans amer math soc 338 1993 105 122 to the nonconvex setting 2006 elsevier inc all rights reserved

existence and characterization of efficient decisions with respect to cones existence and characterization theorems for the efficient nondominated set of decisions inr n are presented the existence is proved when the set of decisions satisfies some compactness conditions the efficient set is characterized in terms of the exposed efficient decisions when certain convexity and compactness conditions are satisfied

relative pareto minimizers for multiobjective problems existence and optimality conditions in this paper we introduce and study enhanced notions of relative pareto minimizers for constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of pareto and weak pareto efficiency minimality using advanced tools of variational analysis and generalized differentiation we establish the existence of relative pareto minimizers for general multiobjective problems under a refined version of the subdifferential palais smale condition for set valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers as well as for conventional efficient and weak efficient counterparts that are new in both finite dimensional and infinite dimensional settings our proofs are based on variational and extremal principles of variational analysis in particular on new versions of the ekeland variational principle and the subdifferential variational principle for set valued and single valued mappings in infinite dimensional spaces

hamiltonian necessary conditions for a multiobjective optimal control problem with endpoint constraints this paper discusses hamiltonian necessary conditions for a nonsmooth multiobjective optimal control problem with endpoint constraints involving a general preference the transversality condition in our necessary conditions is stated in terms of normal cones to the level sets of the preference examples involving a number of useful preferences are discussed

smaller population size at the mrca time for stationary branching processes we consider an elementary model of random size varying population governed by a stationary continuous state branching process we compute the distributions of various variables related to the most recent common ancestor mrca the time to the mrca the size of the current population and the size of the population just before the mrca in particular we observe a natural mild bottleneck effect as the size of the population just before the mrca is stochastically smaller than the size of the current population we also compute the number of individuals involved in the last coalescent event of the genealogical tree that is the number of individuals at the time of the mrca who have descendants in the current population by studying more precisely the genealogical structure of the population we get asymptotics for the number of ancestors just before the current time we give explicit computations in the case of the quadratic branching mechanism in this case the size of the population at the mrca is in mean 2 3 of the size of the current population we also provide in this case the fluctuations for the renormalized number of ancestors

necessary conditions for constrained optimization problems in smooth banach spaces and applications we derive necessary optimality conditions for constrained minimization problems with lower semicontinuous inequality constraints continuous equality constraints and a set constraint in smooth banach spaces then we apply these necessary optimality conditions to derive subdifferential characterizations of singular normal vectors to the epigraph and the graph of a function subdifferential calculus and necessary optimality conditions for mathematical programs with equilibrium constraints

branching processes in levy processes the exploration process the main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure the exploration process appears as a simple local time functional of a levy process with no negative jumps whose laplace exponent coincides with the branching mechanism function this new relation between spectrally positive levy processes and continuous branching processes provides a unified perspective on both theories in particular we derive the adequate formulation of the classical ray knight theorem for such levy processes as a consequence of this theorem we show that the path continuity of the exploration process is equivalent to the almost sure extinction of the branching process

dna ternary addition abstract in this paper we first show a dna representation of a ternary number with digit set 1 0 1 which features its address and each bit position based on this dna representation operations for value assigning and bit position shifting are proposed the algorithm of dna computing for adding two ternary integers is presented the algorithm works in o m steps for adding two ternary integers of m bits

lagrange necessary conditions for pareto minimizers in asplund spaces and applications abstract in this paper new necessary conditions for pareto minimal points to sets and pareto minimizers for constrained multiobjective optimization problems are established without the sequentially normal compactness property and the asymptotical compactness condition imposed on closed and convex ordering cones in bao and mordukhovich 10 and durea and dutta 5 respectively our approach is based on a version of the separation theorem for nonconvex sets and the subdifferentials of vector valued and set valued mappings furthermore applications in mathematical finance and approximation theory are discussed

the standard additive coalescent regard an element of the set x 1 x 2 x 1 x 2 0 i x i 1 as a fragmentation of unit mass into clusters of masses x i the additive coalescent of evans and pitman is the valued markov process in which pairs of clusters of masses x i x j merge into a cluster of mass x i x j at rate x i x j they showed that a version x t t of this process arises as a n weak limit of the process started at time 1 2 log n with n clusters of mass 1 n we show this standard additive coalescent may be constructed from the continuum random tree of aldous by poisson splitting along the skeleton of the tree we describe the distribution of x t on at a fixed time t we show that the size of the cluster containing a given atom as a process in t has a simple representation in terms of the stable subordinator of index 1 2 as t we establish a gaussian limit for centered and normalized cluster sizes and study the size of the largest cluster

necessary suboptimality and optimality conditions via variational principles the paper aims to develop some basic principles and tools of nonconvex variational analysis with applications to necessary suboptimality and optimality conditions for constrained optimization problems in infinite dimensions we establish a certain subdifferential variational principle as a new characterization of asplund spaces this result is different from conventional support forms of variational principles and appears to be convenient for applications to nonsmooth optimization based on the subdifferential variational principle we obtain new necessary conditions for suboptimal solutions in general nonsmooth optimization problems with equality inequality and set constraints in asplund spaces in this way we establish the so called sequential normal compactness properties of constraint sets that play an essential role in infinite dimensional variational analysis and its applications as a by product of our approach we derive various forms of necessary optimality conditions for nonsmooth constrained problems in infinite dimensions which extend known results in that direction

an extended extremal principle with applications to multiobjective optimization we develop an extended version of the extremal principle in variational analysis that can be treated as a variational counterpart to the classical separation results in the case of nonconvex sets and which plays an important role in the generalized differentiation theory and its applications to optimization related problems the main difference between the conventional extremal principle and the extended version developed below is that instead of the translation of sets involved in the extremal systems we allow deformations the new version seems to be more flexible in various applications and covers in particular multiobjective optimization problems with general preference relations in this way we obtain new necessary optimality conditions for constrained problems of multiobjective optimization with nonsmooth data and also for multiplayer multiobjective games

a lamperti type representation of continuous state branching processes with immigration guided by the relationship between the breadth first walk of a rooted tree and its sequence of generation sizes we are able to include immigration in the lamperti representation of continuous state branching processes we provide a representation of continuous state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent levy processes stability of the solutions is studied and gives in particular limit theorems of a type previously studied by grimvall kawazu and watanabe and by li and a simulation scheme for continuous state branching processes with immigration we further apply our stability analysis to extend pitman s limit theorem concerning galton watson processes conditioned on total population size to more general offspring laws

a continuum tree valued markov process we present a construction of a levy continuum random tree crt associated with a super critical continuous state branching process using the so called exploration process and a girsanov theorem we also extend the pruning procedure to this super critical case let be a critical branching mechanism we set let or be the set of values of for which is a conservative branching mechanism the pruning procedure allows to construct a decreasing levy crt valued markov process mathcal t theta theta in theta such that mathcal t theta has branching mechanism it is sub critical if 0 and super critical if 0 we then consider the explosion time a of the crt the smallest negative time for which the continuous state branching process cb associated with mathcal t theta has finite total mass i e the length of the excursion of the exploration process that codes the crt is finite we describe the law of a as well as the distribution of the crt just after this explosion time the crt just after explosion can be seen as a crt conditioned not to be extinct which is pruned with an independent intensity related to a we also study the evolution of the crt valued process after the explosion time this extends results from aldous and pitman on galton watson trees for the particular case of the quadratic branching mechanism we show that after explosion the total mass of the cb behaves like the inverse of a stable subordinator with index 1 2 this result is related to the size of the tagged fragment for the fragmentation of aldous s crt

the lagrange multiplier rule for super efficiency in vector optimization in this paper we study constrained multiobjective optimization problems with objectives being closed graph multifunctions in banach spaces in terms of the coderivatives and clarke s normal cones we establish lagrange multiplier rules for super efficiency as necessary or sufficient optimality conditions of the above problems

a polynomial time dna computing solution for the bin packing problem it is suggested here an algorithm based on stickers for the dna computing model s roweis e winfree r burgoyne n chelyapov m goodman p rothemund l adleman a sticker based model for dna computation journal of computational biology 5 1998 615 629 that solves the well known bin packing problem bpp that belongs to the class np hard in the strong sense in a time bounded by o n 2q where n is the quantity of items and q the space requirements expressed in bits to the best of the authors knowledge this is the first polynomial time algorithmic solution for the bpp in such a model

on the existence of pareto efficient points we prove some general theorems on the existence of minimal points of compact sets in linear spaces with respect to closed convex orderings these results are compared to the axiom of choice

a fuzzy necessary optimality condition for non lipschitz optimization in asplund spaces in this paper we consider a general optimization problem in the broad class of asplund spaces we derive a new necessary optimality condition in the so called lagrangian fuzzy form without standard lipschitz conditions we also give a chain rule for frechet subdifferentials and subdifferential representations of frechet normals to constrained sets