estimation in capture recapture models when covariates are subject to measurement errors nous considerons les problemes d estimation des modeles de capture recapture quand les covariables ou les variables auxilliaires sont mesurees avec erreur nous trouvons que l approche naive qui ignore les erreurs de mesure est inacceptable pour l estimation des parametres de regression et de la taille de la population elle donne des estimateurs biaises de manieere croissante avec l amplitude des erreurs et des intervalles de confiance fausses pour tenir compte des erreurs de mesure nous proposons un estimateur des parametres de regression par une methode de calibration et developpons des estimateurs modifies de la taille de la population une etude de simulation montre que les estimateurs resultants sont plus satisfaisant que ceux de l approche naive ou de la methode d extrapolation simulation simex des donnees de l espece d oiseau primia flaviventris a hong kong sont analysees avec et sans l hypothese d erreur de mesure pour demontrer l effet des erreurs sur les estimations

the isomorphism conjecture fails relative to a random oracle berman and hartmanis 1977 conjectured that there is a polynomial time computable isomorphism between any two languages complete for np with respect to polynomial time computable many one karp reductions joseph and young 1985 gave a structural definition of a class of np complete sets the k creative sets and defined a class of sets the k f k s that are necessarily k creative they went on to conjecture that certain of these k f t s are not isomorphic to the standard np complete sets clearly the berman hartmanis and joseph young conjectures cannot both be correct we introduce a family of strong one way functions the scrambling functions if f is a scrambling function then k f k is not isomorphic to the standard np complete sets as joseph and young conjectured and the berman hartmanis conjecture fails indeed if scrambling functions exist then the isomorphism also fails at higher complexity classes such as exp and nexp as evidence for the existence of scrambling functions we show that much more powerful one way functions the annihilating functions exist relative to a random oracle random oracles are the first examples of oracles relative to which the isomorphism conjecture fails with respect to higher classes such as exp and nexp

a uniform approach to obtain diagonal sets in complexity classes abstract a uniform method for constructing sets which diagonalize over certain complexity classes while preserving other complexity properties is given we obtain some known results as well as some new ones as corollaries of our main theorem the new results concern the complexity classes p np co np pspace apt almost polynomial time r random polynomial time and the polynomial hierarchy

differentiability of the metric projection in hilbert space a study is made of differentiability of the metric projection p onto a closed convex subset k of a hilbert space h when k has nonempty interior the gateaux or fr het smoothness of its boundary can be related with some precision to gateaux or frechet differentiability properties of p for instance combining results in 3 with earlier work of r d holmes shows that k has a c2 boundary if and only if p is cl in h k and its derivative p has a certain invertibility property at each point an example in 5 shows that if the c2 condition is relaxed even slightly then p can be nondifferentiable fr het in h k

kolmogorov complexity and degrees of tally sets we show that either epm tally epbtt tally or epm tally ep1 tt tally ep2 tt tally ep3 tt tally where erp tally denotes the class of sets which are equivalent to a tally set under rp reductions furthermore the question of whether or not emp tally ebttp tally is equivalent to the question of whether or not ne predicates can be solved in deterministic exponential time the proofs use the techniques of generalized kolmogorov complexity as corollaries to some of the main results we obtain new results about the kolmogorov complexity of sets in p

a semiparametric method for estimating population size for capture recapture experiments with random covariates in continuous time a semiparametric estimation procedure is proposed to model capture recapture data with the aim of estimating the population size for a closed population individuals covariates are possibly time dependent and missing at noncaptured times and may be measured with error a set of estimating equations ees based on covariate process and capture recapture data is constructed to estimate the relevant parameters and the population size these ees can be solved by an algorithm similar to an em algorithm simulation results show that the proposed procedures work better than the naive estimate in some cases they are even better than ideal estimates for which the true values of covariates are available for all captured subjects over the entire experimental period we apply the method to a capture recapture experiment on the bird species prinia flaviventris in hong kong

padding commitment and self reducibility abstract a new property of np sets called commitability is introduced in this paper roughly a language l in np is commitable if given any instance x and any string y a string z can be found in polynomial time such that z is in l iff y is a prefix of a witness of x in the context of a ptime relation that defines l it is shown that all np sets complete under polynomial time many one reductions are commitable commitability can be seen as a genralization of d self reducibility every d self reducible set is commited and yet commitability retains an important aspect of d self reducibility the tree search method of berman is shown to be extendible to commitable sets therefore certain known results about reductions to co sparse sets and p selective sets generalize from d self reductible sets to commitable sets the connection with paddability is as follows every paddable and commitable set is shown to be d self reducible it is also shown that paddability in np implies kernel constructibility which was introduced elsewhere to capture a notion of self reducibility more general than d self reducibility

spectrum and analytical indices of the c algebra of wiener hopf operators we study multivariate generalisations of the classical wiener hopf algebra which is the c algebra generated by the wiener hopf operators given by convolutions restricted to convex cones by the work of muhly and renault this c algebra is known to be isomorphic to the reduced c algebra of a certain restricted action groupoid given by the action of euclidean space on a certain compactification using groupoid methods we construct composition series for the wiener hopf c algebra by a detailed study of this compactification we compute the spectrum and express homomorphisms in k theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms namely these symbols maps turn out to be given by an analytical family index of a continuous family of fredholm operators in a subsequent paper we also obtain a topological expression of these indices

on p creative sets and p completely creative sets abstract we study p creative sets and p completely creative sets we first prove that for recursively enumerable sets p creativeness is equivalent to p complete creativeness and myhill s theorem still holds in the polynomial setting we then consider p creativity and p complete creativity for time complexity classes we prove that for p p creativeness is equivalent to p complete creativeness moreover we prove that a set a is p m complete for dext iff a is p creative for p in dext since every p m complete set for dext is p 1 complete berman 1977 we know that myhill s theorem still holds for p in dext these results can also be proved for np in next k creative sets and k completely creative sets in np are next studied k l creative sets and k l completely creative sets in a more general setting are defined and shown to exist it is known that k completely creative sets are np complete joseph and young 1985 but it is not known whether the converse is true we approach this problem based on our double diagonalization technique of showing that every p m complete set for dext is p creative for p a new class of k completely creative sets is constructed as well

smoothness of the metric projection onto nonconvex bodies in hilbert spaces abstract based on a fundamental work of r b holmes from 1973 we study differentiability properties of the metric projection onto prox regular sets we show that if the set is a nonconvex body with a c p 1 smooth boundary then the projection is c p smooth near suitable open truncated normal rays which are determined only by the function of prox regularity a local version of the same result is established as well namely when the smoothness of the boundary and the prox regularity of the set are assumed only near a fixed point finally similar results are derived when the prox regular set is itself a c p 1 submanifold

perturbed optimization in banach spaces iii semi infinite optimization this paper is devoted to the study of perturbed semi infinite optimization problems i e minimization over er n with an infinite number of inequality constraints we obtain the second order expansion of the optimal value function and the first order expansion of approximate optimal solutions in two cases i when the number of binding constraints is finite and ii when the inequality constraints are parametrized by a real scalar these results are partly obtained by specializing the sensitivity theory for perturbed optimization developed in part i cf siam j control optim 34 1996 pp 1151 1171 and deriving specific sharp lower estimates for the optimal value function which take into account the curvature of the positive cone in the space c omega of continuous real valued functions

nondegeneracy and quantitative stability of parameterized optimization problems with multiple solutions this paper presents some results on quantitative stability of optimal solutions of parameterized optimization problems having nonisolated optima the analysis is based on the introduced concept of nondegeneracy which may be of independent interest examples of nonlinear and semidefinite programming are discussed

directional differentiability of the optimal value function in convex semi infinite programming in this paper directional differentiability properties of the optimal value function of a parameterized semi infinite programming problem are studied it is shown that if the unperturbed semi infinite programming problem is convex then the corresponding optimal value function is directionally differentiable under mild regularity assumptions a max min formula for the directional derivatives well known in the finite convex case is given

complexity classes without machines on complete languages for up this paper develops techniques for studying complexity classes that are not covered by known recursive enumerations of machines often counting classes probabilistic classes and intersection classes lack such enumerations concentrating on the counting class up we show that there are relativizations for which upa has no complete languages and other relativizations for which pb upb npb and upb has complete languages among other results we show that p up if and only if there exists a set s in p of boolean formulas with at most one satisfying assignment such that s sat is not in p p up coup if and only if there exists a set s in p of uniquely satisfiable boolean formulas such that no polynomial time machine can compute the solutions for the formulas in s if up has complete languages then there exists a set r in p of boolean formulas with at most one satisfying assignment so that sat r is complete for up finally we indicate the wide applicability of our techniques to counting and probabilistic classes by using them to examine the probabilistic class bpp there is a relativized world where bppa has no complete languages if bpp has complete languages then it has a complete language of the form b majority where b p and majority f f is true for at least half of all assignments is the canonical pp complete set

full likelihood inference for abundance from continuous time capture recapture data capture recapture experiments are widely used cost effective sampling techniques for estimating population sizes or abundances in biology ecology demography epidemiology and reliability studies for continuous time capture recapture data existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation the corresponding wald type confidence intervals for the abundance may have severe undercoverage and their lower limits can be below the number of individuals captured we propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood under both parametric and semiparametric intensity models we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically 2 with 1 degree of freedom simulations indicate that compared with conditional likelihood based methods the maximum full likelihood estimator has a smaller mean square error and the likelihood ratio confidence intervals often have remarkable gains in coverage probability we illustrate the advantages of the proposed approach by analysing illegal immigrant data for the netherlands and prinia flaviventris data from hong kong

resource bounded immunity and simplicity revisiting the 30 years old notions of resource bounded immunity and simplicity we investigate the structural characteristics of various immunity notions strong immunity almost immunity and hyperimmunity as well as their corresponding simplicity notions we also study limited immunity and simplicity called k immunity and feasible k immunity and their simplicity notions finally we propose the k immune hypothesis as a working hypothesis that guarantees the existence of simple sets in np

optimal control problems with partially polyhedric constraints this paper discusses a class of state constrained optimal control problems for which it is possible to formulate second order necessary or sufficient conditions for local optimality or quadratic growth that do not involve all curvature terms for the constraints this kind of result is classical in the case of polyhedric control constraints our theory of optimization problems with partially polyhedric constraints allows to extend these results to the case when the control constraints are polyhedric in the presence of state constraints satisfying some specific hypotheses the analysis is based on the assumption that some strict semilinearized qualification condition is satisfied we apply the theory to some optimal control problems of elliptic equations with state and control constraints

a quadratically convergent algorithm for convex set constrained signal recovery this paper addresses the problem of recovering a signal that is constrained to lie in a convex set from linear measurements the current standard is the alternating projections paradigm pocs which has only first order convergence in general we present a quadratically convergent iterative algorithm newton algorithm for signal recovery from linear measurements and convex set constraints a new result on the existence and construction of the derivative of the projection operator onto a convex set is obtained which is used in the newton algorithm an interesting feature of the new algorithm is that each iteration requires the solution of a simpler subspace constrained reconstruction problem a computation and memory efficient version of the algorithm is also obtained by using the conjugate gradient algorithm within each newton iteration to avoid matrix inversion and storage from a computational point of view the computation per iteration of this algorithm is similar to the computation per iteration of the standard alternating projections algorithm the faster rate of convergence compared to alternating projections enables us to obtain a high resolution reconstruction with fewer computations the algorithm is thus well suited for large scale problems that typically arise in image recovery applications the algorithm is demonstrated in several applications

perturbed optimization in banach spaces i a general theory based on a weak directional constraint qualification using a directional form of constraint qualification weaker than robinson s we derive an implicit function theorem for inclusions and use it for first and second order sensitivity analyses of the value function in perturbed constrained optimization we obtain holder and lipschitz properties and under a no gap condition first order expansions for exact and approximate solutions as an application differentiability properties of metric projections in hilbert spaces are obtained using a condition generalizing polyhedricity we also present in the appendix a short proof of a generalization of the convex duality theorem in banach spaces

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

no gap second order optimality conditions for optimal control problems with a single state constraint and control the paper deals with optimal control problems with only one control variable and one state constraint of arbitrary order we consider the case of finitely many boundary arcs and touch times we obtain a no gap theory of second order conditions allowing to characterize second order quadratic growth

stability analysis of optimal control problems with a second order state constraint this paper gives stability results for nonlinear optimal control problems subject to a regular state constraint of second order the strengthened legendre clebsch condition is assumed to hold and no assumption on the structure of the contact set is made under a weak second order sufficient condition taking into account the active constraints we show that the solutions are lipschitz continuous w r t the perturbation parameter in the l 2 norm and holder continuous in the l infty norm we use a generalized implicit function theorem in metric spaces by dontchev and hager siam j control optim 36 1998 pp 698 718 the difficulty is that multipliers associated with second order state constraints have a low regularity they are only bounded measures we obtain lipschitz stability of a primitive of the state constraint multiplier

measurement errors in line transect surveys where detectability varies with distance and size summary when using bivariate line transect methods to estimate the biomass density of a tightly clustered biological population it is generally assumed that both the perpendicular distance from the trackline to the cluster and the cluster size or biomass are measured without error this is unlikely to be the case in practice in this article assuming additive mean zero errors in distance and multiplicative errors in size we develop an estimator of density that corrects for these errors we use the method of moments for the case of gamma cluster size randomly placed transect lines and the generalized exponential detection function we derive results that show that it may not be necessary to correct for errors in distance or size when the distance and size estimates are not biased when the size estimates are biased the biomass density estimate has approximately the same bias as the size estimates the work is illustrated in the context of annual aerial surveys for juvenile southern bluefin tuna in the great australian bight

on sensitivity analysis of nonlinear programs in banach spaces the approach via composite unconstrained optimization this article studies local sensitivity analysis of nonlinear programming problems in banach spaces with arbitrary sets of solutions and no a priori regularity properties this is done by first developing a corresponding theory for unconstrained optimization involving simple composite functions and then applying this theory to general nonlinear programs by way of certain reduction principles

robust design and the use of auxiliary variables in estimating population size for an open population nous considerons le probleme de l estimation de la taille d une population ouverte ou les donnees sont collectees sur une deuxieme periode a l interieur d une periode primaire selon un plan robuste propose par pollock 1982 une vraisemblance conditionnelle est utilisee pour estimer les parametres associes a un modele lineaire generalise pour lequel la probabilite de capture est supposee suivre une loi logistique qui depend de covariables individuelles un estimateur de type horvitz thompson est utilise pour estimer la taille de la population pour chaque periode primaire et les probabilites du survie entre les periodes primaires les proprietes asymptotiques de l estimateur propose explorees par simulation ont de bonnes proprietes un jeu de donnee attache a une etude de capture recapture de petits mammiferes conduite selon un plan robuste a dummy bottom au sein du browns park national wildlife refuge est analyse

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

differential stability of two stage stochastic programs two stage stochastic programs with random right hand side are considered optimal values and solution sets are regarded as mappings of the expected recourse functions and their perturbations respectively conditions are identified implying that these mappings are directionally differentiable and semidifferentiable on appropriate functional spaces explicit formulas for the derivatives are derived special attention is paid to the role of a lipschitz condition for solution sets as well as of a quadratic growth condition of the objective function

on simple and creative sets in np abstract two structurally defined types of np sets are studied k simple sets are defined and shown to exist in np other properties of these sets are investigated k creative sets as previously defined by joseph and young 1985 are next considered a new condition is given which implies that a set is k creative several previously considered np complete sets are proved to be k creative

conjugate duality in set valued vector optimization abstract in this paper conjugate duality results for convexlike set valued vector optimization problems are presented under closedness or boundedness hypotheses some properties of the value mapping of a set valued vector optimization problem are studied a conjugate duality result is also proved for a convex set valued vector optimization problem without the requirements of closedness and boundedness

maximum likelihood abundance estimation from capture recapture data when covariates are missing at random in capture recapture experiments individual covariates may be subject to missingness especially when the number of captures is small when the covariate information is missing at random the inverse probability weighting method and the multiple imputation method are widely used to obtain point estimators of the abundance these estimators are then used to construct wald type confidence intervals however such intervals may have seriously inaccurate coverage probabilities in this paper we propose a maximum empirical likelihood el estimation approach for the abundance in the presence of missing covariates we show that the maximum el estimator is asymptotically normal and that the el ratio statistic for the abundance has a chi square limiting distribution with one degree of freedom simulations indicate that the proposed estimator has a smaller mean square error than existing estimators and the proposed el ratio confidence interval usually has more accurate coverage probabilities than the existing wald type confidence intervals we illustrate the proposed method by analyzing data collected in hong kong for the yellow bellied prinia a bird species

second order optimality conditions based on parabolic second order tangent sets in this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints our analysis is based on various concepts of second order tangent sets and parametric duality we introduce a condition called second order regularity under which there is no gap between the corresponding second order necessary and second order sufficient conditions we show that the second order regularity condition always holds in the case of semidefinite programming

exponential time and subexponential time sets abstract in this paper we prove that the symmetric difference of a p k parity hard set for e and a subexponential time computable set is still p k parity hard for e this remains true for p m hard set for e since a 1 parity reduction is a many one reduction in addition we show that this property fails to hold for some other types of reductions we introduce and study the notions of e complete kernel and e hard kernel

some relaxation problems in optimal control theory usually the space u r is a space lp q endowed with its weak topology the space y g is a sobolev space w y q endowed with its weak topology or with the l q topology in the one dimensional case and condition ii is guaranteed by some boundedness or growth hypotheses on j and a when condition i is not fulfilled in general the existence of a solution of 1 1 may fail nevertheless it may be interesting to study the asymptotic 212 0022 247x 87 3 00

quantitative stability of variational systems ii a framework for nonlinear conditioning stability results of lipschitz and holder type are obtained for the solutions and optimal values of optimization problems when perturbations are measured in terms of the rho epi distance

completeness approximation and density polynomial time approximations to exponential time computable problems exp are considered from the point of view of structure infinitely often speedable and almost everywhere complex problems are studied using the notions of polynomial time productivity and immunity in particular the existence of a polynomial time immune set which is not polynomial time approximable at all but which is polynomial time tt complete in exp is proven the relationship between completeness and approximability is also studied it is shown that being polynomial time m complete in exp does not provide any control of the probability of erroneous approximations

perturbed optimization in banach spaces ii a theory based on a strong directional constraint qualification we study the sensitivity of the optimal value and optimal solutions of perturbed optimization problems in two cases the first one is when multipliers exist but only the weak and not the strong second order sufficient optimality condition is satisfied the second case is when no lagrange multipliers exist to deal with these pathological cases we are led to introduce a directional constraint qualification stronger than in part i of this paper which reduces to the latter in the important case of equality inequality constrained problems we give sharp upper estimates of the cost based on paths varying as the square root of the perturbation parameter and under a no gap condition obtain the first term of the expansion for the cost when multipliers exist we study the expansion of approximate solutions as well we show in the appendix that the strong directional constraint qualification is satisfied for a large class of problems including regular problems in the sense of robinson

reductions among polynomial isomorphism types abstract a set a is polynomial many one reducible to a set b a is karp reducible to b if there is a polynomially computable function f such that for all x x a iff f x b arbitrary sets a and b are of the same polynomial many one degree if each is polynomial many one reducible to the other a and b are polynomially isomorphic if the function f can be taken one to one onto and polynomially invertible in classical recursive function theory all many one complete sets are recursively isomorphic berman and hartmanis have observed that all known np complete sets are polynomially isomorphic berman and hartmanis have observed that all known np complete sets are polynomially isomorphic and have conjectured that all np complete sets complete under karp reducibility are isomorphic in this paper we show that not just the complete degree but every polynomial many one degree consists either of a single isomorphism type or else contains infinitely many isomorphism types densely ordered under one one size increasing polynomially invertible reductions and also contains infinitely many isomorphisms types which are incomparable under one one invertible reductions in fact we show that every countable partial ordering can be embedded in any such many one degree we also exhibit polynomial degrees which have infinitely many isomorphism types no examples are known of degrees consisting of a single isomorphism type

on the topological size of p m complete degrees abstract all polynomial many one degrees are shown to be of second baire category in the superset topology when witness functions are allowed to run in 2loghn time for any h any improvement of this result for the complete p m degrees of re exp or np implies p np or the nonisomorphism of the np complete sets

optimal control of a parabolic equation with time dependent state constraints in this paper we study the optimal control problem of the heat equation with a cubic nonlinearity by a distributed control over a subset of the domain in the presence of a state constraint the latter is integral over the space and has to be satisfied each time using for the first time the technique of alternative optimality systems in the context of optimal control of partial differential equations we show that both the control and multiplier are continuous in time under some natural geometric hypotheses we can prove that extended polyhedricity holds allowing us to obtain no gap second order optimality conditions that characterize quadratic growth an expansion of the value function and of approximate solutions can be computed for a directional perturbation of the right hand side of the state equation

maximum empirical likelihood estimation for abundance in a closed population from capture recapture data summarycapture recapture experiments are widely used to collect data needed for estimating the abundance of a closed population to account for heterogeneity in the capture probabilities huggins 1989 and alho 1990 proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified a conditional likelihood method was then proposed to obtain point estimates and wald type confidence intervals for the abundance empirical studies show that the small sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right which may produce wald type confidence intervals with lower limits that are less than the number of captured individuals or even are negative in this paper we propose a full empirical likelihood approach based on huggins and alho s model we show that the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi squared with one degree of freedom and that the maximum empirical likelihood estimator achieves semiparametric efficiency simulation studies show that the empirical likelihood based method is superior to the conditional likelihood based method its confidence interval has much better coverage and the maximum empirical likelihood estimator has a smaller mean square error we analyse three datasets to illustrate the advantages of our empirical likelihood approach

on one way functions and polynomial time isomorphisms it is shown that if one way functions exist then there are sets a and b such that a and b are equivalent under one one and length increasing polynomial time reductions and such that a is not polynomial time isomorphic to b furthermore sets a and b can be constructed such that they are polynomial time truth table complete for the class of exponential time computable sets

sensitivity analysis of optimization problems under second order regular constraints we present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition this is a technical condition that is always satisfied in the case of semi definite optimization we derive lipschitz and holder expansions of approximate optimal solutions under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem we show how the theory applies to semi infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds and discuss the differentiability of metric projections as well as the moreau yosida regularization finally we show how the theory applies to semi definite optimization

some remarks on witness functions for nonpolynomial and noncomplete sets in np abstract we present two results about witness functions for sets in np and conp first any set that has a polynomially computable function which witnesses that it is not in conp must be at least np hard it follows from this result that any set in np conp that has a polynomially computable function which witnesses this fact must already be complete for np second if b is any set for which there is a polynomially computable function which witnesses that it is not complete for np by witnessing that some fixed set in np is not in p b then b must already be in np conp thus for two sets in np conp there are no polynomially computable functions which witness that one is not polynomially reducible to the other in proving the first result we introduce the notion of a k creative set and prove that all k creative sets are np complete since these sets seem not to be all polynomially isomorphic we counter the conjecture of berman and hartmanis that all np complete sets are isomorphic to sat with our own conjecture that not all k creative sets are isomorphic to sat the proofs we give are recursion theoretic in style but straightforward

relaxation of constrained control problems the problem of relaxation of optimal control problems with state and control constraints is formulated in this paper we determine that if the original problem consists of minimizing over control functions z g x t subject to d x ds f s x z t s leq t and h s x s z s leq 0 for a e t leq s leq t then the relaxed problem consists of minimizing over measure valued control functions m g xhat t subject to d xhat ds int z f s xhat s z m s dz and m s esssup z h s xhat s z leq 0 for a e t leq s leq t for each s this is the essential supremum of h in z with respect to the measure m s

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

on inefficient special cases of np complete problems abstract every intractable set a has a polynomial complexity core a set h such that for any p subset s of a or of s h is finite a complexity core h of a is proper if h a it is shown here that if p np then every currently known i e either invertibly paddable or k creative np complete set a and its complement have proper polynomial complexity cores that are nonsparse and are accepted by deterministic machines in time 2 cn for some constant c turning to the intractable class d ext c 0 d time 2 cn it is shown that every set that is p m complete for d ext has an infinite proper polynomial complexity core that is nonsparse and recursive

pseudopower expansion of solutions of generalized equations and constrained optimization problems we show that the solution of a strongly regular generalized equation subject to a scalar perturbation expands in pseudopower series in terms of the perturbation parameter i e the expansion of orderk is the solution of generalized equations expanded to orderk and thus depends itself on the perturbation parameter in the polyhedral case this expansion reduces to a usual taylor expansion these results are applied to the problem of regular perturbation in constrained optimization we show that if the strong regularity condition is satisfied the property of quadratic growth holds and at least locally the solutions of the optimization problem and of the associated optimality system coincide if in addition the number of inequality constraints is finite the solution and the lagrange multiplier can be expanded in taylor series if the data are analytic the solution and the multiplier are analytic functions of the perturbation parameter

optimal approximations and polynomially levelable sets a set a not in p is polynomially levelable if any algorithm for a has speedup to a polynomial infinitely often in a precisely if given any algorithm m for a and polynomial p it is possible to find another algorithm m for a and polynomial p such that m runs in time p x on infinitely many inputs x in a on which the running time of m exceeds p x intuitively this condition states that among polynomial time computable approximations to a there is no optimal one or one giving correct answers on a maximally large subset of a it appears that most naturally occurring intractable sets are polynomially levelable we prove this for sets not in p that are either paddable self reducible or complete for a deterministic time class we also discuss levelability preserving reductions and give a simple reducibility characterization of nonlevelable sets

a first order isomorphism theorem we show that for most complexity classes of interest all sets complete under first order projections fops are isomorphic under first order isomorphisms that is a very restricted version of the berman hartmanis conjecture holds since natural complete problems seem to stay complete via fops this indicates that up to first order isomorphism there is only one natural complete problem for each nice complexity class

second order necessary conditions in pontryagin form for optimal control problems in this article we state and prove first and second order necessary conditions in pontryagin form for optimal control problems with pure state and mixed control state constraints we say that a lagrange multiplier of an optimal control problem is a pontryagin multiplier if it is such that pontryagin s minimum principle holds and we call optimality conditions in pontryagin form those which only involve pontryagin multipliers our conditions rely on a technique of partial relaxation and apply to pontryagin local minima

sensitivity analysis for relaxed optimal control problems with final state constraints in this article we compute a second order expansion of the value function of a family of relaxed optimal control problems with final state constraints parameterized by a perturbation variable the sensitivity analysis is performed for controls that we call r strong solutions they are optimal solutions with respect to the set of feasible controls with a uniform norm smaller than a given r and having an associated trajectory in a small neighborhood for the uniform norm in this framework relaxation enables us to consider a wide class of perturbations and therefore to derive sharp estimates of the value function

relaxation of control systems under state constraints in this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control in particular we show that the mangasarian fromowitz constraint qualification allows us to rewrite constrained systems as differential inclusions with locally lipschitz right hand side then the filippov wazewski relaxation theorem may be applied to show that ordinary solutions are dense in the set of relaxed solutions if besides agreeing with the above constraints the state has to remain in a control independent set k then the mangasarian fromowitz condition cannot hold this case is investigated as well by means of a condition on the feasible velocities on the boundary of k

on the p isomorphism conjecture watanabe o on the p isomorphism conjecture note theoretical computer science 83 1991 337 343

on the marginal function in nonlinear programming for several types of finite or infinite dimensional optimization problems the marginal function or optimal value function is characterized by different local approximations such as generalized gradients generalized directional derivatives directional hadamard or dini derivatives we give estimates for these terms which are determined by multipliers satisfying necessary optimality conditions when the functions which define the optimization problem are more than once continuously differentiable then higher order necessary conditions are employed to obtain refined estimates for the marginal function as a by product we give a new equivalent formulation of clarke s multiplier rule for nonsmooth optimization problems this shows that the set of all multipliers satisfying these necessary conditions is the union of a finite number of closed convex cones

the riccati equation for optimal control problems with mixed state control constraints necessity and sufficiency the goal of this paper is to conduct a complete study of second order conditions for the optimal control problem with mixed state control constraints the conjugate point theory is presented and a necessary condition in terms of the corresponding riccati equation is obtained sufficiency criteria are developed in terms of strengthened necessary conditions including the riccati equation the results generalize the known ones for pure control constraints as well as for the mixed state control constraints

viscosity solutions of minimization problems viscosity methods for minimization problems are revisited from some modern perspectives in variational analysis variational convergences for sequences of functions epi convergence gamma convergence mosco convergence and for sequences of operators graph convergence provide a flexible tool for such questions it is proved in a rather large setting that the solutions of the approximate problems converge to a viscosity solution of the original problem that is a solution that is minimal among all the solutions with respect to some viscosity criteria various examples coming from mathematical programming calculus of variations semicoercive elliptic equations phase transition theory hamilton jacobi equations singular perturbations and optimal control theory are considered

differentiability with respect to parameters of solutions to convex programming problems we consider a family of convex programming problems that depend on a vector parameter characterizing those values of parameters at which solutions and associated lagrange multipliers are g teaux differentiable these results are specialized to the problem of the metric projection onto a convex set at those points where the projection mapping is not differentiable the form of clarke s generalized derivative of this mapping is derived

directional differentiability of metric projections onto moving sets at boundary points soient x y des espaces normes de dimension finie et x y une multifonction assignant a chaque xex un ensemble ferme x cy a x sont associees la fonction distance d x y r et la projection metrique a valeur d ensemble x y y on etudie les proprietes differentielles de au voisinage d un point x 0 y 0 avec y 0 point limite de l ensemble x 0

one way functions and the nonisomorphism of np complete sets abstract the one way conjecture states that the existence of nonisomorphic np complete sets implies the existence of one way functions this paper gives a relativized counterexample to the conjecture by constructing a relativized world that has nonisomorphic np complete sets but lacks one way functions

optimization problems with perturbations a guided tour this paper presents an overview of some recent and significant progress in the theory of optimization problems with perturbations we put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems these methods allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of lagrange multipliers is not a singleton may be unbounded or is even empty we give rather complete results for nonlinear programming problems and describe some extensions of the method to more general problems we illustrate the results by computing the equilibrium position of a chain that is almost vertical or horizontal

one way functions and the isomorphism conjecture abstract the isomorphism conjecture is investigated for exponential time and other complexity classes if one way functions exist then we show that there are one way functions such that a p f a where a is a standard complete set for np or e or ne if one way functions exist we also show that there are k completely creative sets in np with one way productive functions but which are p isomorphic to standard complete sets we then present a type of one way functions whose existence is equivalent to the failure of the isomorphism conjecture for e finally we show that the isomorphism conjecture holds for e ne if and only if it holds for exp nexp