deep feature learning with relative distance comparison for person re identification identifying the same individual across different scenes is an important yet difficult task in intelligent video surveillance its main difficulty lies in how to preserve similarity of the same person against large appearance and structure variation while discriminating different individuals in this paper we present a scalable distance driven feature learning framework based on the deep neural network for person re identification and demonstrate its effectiveness to handle the existing challenges specifically given the training images with the class labels person ids we first produce a large number of triplet units each of which contains three images i e one person with a matched reference and a mismatched reference treating the units as the input we build the convolutional neural network to generate the layered representations and follow with the l 2 distance metric by means of parameter optimization our framework tends to maximize the relative distance between the matched pair and the mismatched pair for each triplet unit moreover a nontrivial issue arising with the framework is that the triplet organization cubically enlarges the number of training triplets as one image can be involved into several triplet units to overcome this problem we develop an effective triplet generation scheme and an optimized gradient descent algorithm making the computational load mainly depend on the number of original images instead of the number of triplets on several challenging databases our approach achieves very promising results and outperforms other state of the art approaches highlightswe present a novel feature learning framework for person re identification our framework is based on the maximum relative distance comparison the learning algorithm is scalable to process large amount of data we demonstrate superior performances over other state of the arts

existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance besides this we obtain two solutions in the case of near resonance

data driven chance constrained stochastic program in this paper we study data driven chance constrained stochastic programs or more specifically stochastic programs with distributionally robust chance constraints dccs in a data driven setting to provide robust solutions for the classical chance constrained stochastic program facing ambiguous probability distributions of random parameters we consider a family of density based confidence sets based on a general phi divergence measure and formulate dcc from the perspective of robust feasibility by allowing the ambiguous distribution to run adversely within its confidence set we derive an equivalent reformulation for dcc and show that it is equivalent to a classical chance constraint with a perturbed risk level we also show how to evaluate the perturbed risk level by using a bisection line search algorithm for general phi divergence measures in several special cases our results can be strengthened such that we can derive closed form expressions for the perturbed risk levels in addition we show that the conservatism of dcc vanishes as the size of historical data goes to infinity furthermore we analyze the relationship between the conservatism of dcc and the size of historical data which can help indicate the value of data finally we conduct extensive computational experiments to test the performance of the proposed dcc model and compare various phi divergence measures based on a capacitated lot sizing problem with a quality of service requirement

uncertain convex programs randomized solutions and confidence levels many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or instance parameter two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty robust optimization and chance constrained optimization robust optimization is a deterministic paradigm where one seeks a solution which simultaneously satisfies all possible constraint instances in chance constrained optimization a probability distribution is instead assumed on the uncertain parameters and the constraints are enforced up to a pre specified level of probability unfortunately however both approaches lead to computationally intractable problem formulations

socially constrained structural learning for groups detection in crowd modern crowd theories agree that collective behavior is the result of the underlying interactions among small groups of individuals in this work we propose a novel algorithm for detecting social groups in crowds by means of a correlation clustering procedure on people trajectories the affinity between crowd members is learned through an online formulation of the structural svm framework and a set of specifically designed features characterizing both their physical and social identity inspired by proxemic theory granger causality dtw and heat maps to adhere to sociological observations we introduce a loss function g mitre able to deal with the complexity of evaluating group detection performances we show our algorithm achieves state of the art results when relying on both ground truth trajectories and tracklets previously extracted by available detector tracker systems

resonance problems for the p laplacian systems abstract two existence theorems of the solutions are obtained for the p laplacian systems at resonance under a landesman lazer type condition by critical point theory

some existence theorems for elliptic resonant problems some existence theorems are obtained for the elliptic resonant problems at either the first eigenvalue or the higher eigenvalues with unbounded nonlinearity by using the minimax methods in critical point theory

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

concavity and efficient points of discrete distributions in probabilistic programming we consider stochastic programming problems with probabilistic constraints involving integer valued random variables the concept of a p efficient point of a probability distribution is used to derive various equivalent problem formulations next we introduce the concept of r concave discrete probability distributions and analyse its relevance for problems under consideration these notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables the results are illustrated with numerical examples

existence of multiple solutions for a class of p q laplacian systems abstract we establish the existence and multiplicity of solutions for some p q laplacian systems we will show how the multiplicity of solutions change as and vary the results are proved by ekeland s variational principle the mountain pass theorem and the saddle point theorem

a model for dynamic chance constraints in hydro power reservoir management in this paper a model for joint dynamic chance constraints is proposed and applied to an optimization problem in water reservoir management the model relies on discretization of the decision variables but keeps the probability distribution continuous our approach relies on calculating probabilities of rectangles which is particularly useful in the presence of independent random variables but works for a moderate number of stages equally well in case of correlated variables numerical results are provided for two and three stages

resonance problems for p q laplacian systems abstract some existence results of weak solutions are established for p q laplacian systems which are resonant at an arbitrary eigenvalue by the minimax methods in critical point theory

the probabilistic set covering problem in a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability we analyze the structure of the set of probabilistically efficient points of binary random vectors develop methods for their enumeration and propose specialized branch and bound algorithms for probabilistic set covering problems

resonance problems for the p laplacian with a nonlinear boundary condition abstract consider resonance problems at an arbitrary eigenvalue of the elliptic equations p u u p 2 u g 1 u h 1 x in u p 2 u u p 2 u g 2 u h 2 x on some existence theorems are obtained under the landesman lazer type conditions by using variational method

the exact feasibility of randomized solutions of uncertain convex programs many optimization problems are naturally delivered in an uncertain framework and one would like to exercise prudence against the uncertainty elements present in the problem in previous contributions it has been shown that solutions to uncertain convex programs that bear a high probability to satisfy uncertain constraints can be obtained at low computational cost through constraint randomization in this paper we establish new feasibility results for randomized algorithms specifically the exact feasibility for the class of the so called fully supported problems is obtained it turns out that all fully supported problems share the same feasibility properties revealing a deep kinship among problems of this class it is further proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully supported problems the feasibility result of this paper outperforms previous bounds and is not improvable because it is exact for fully supported problems

multiplicity of solutions for resonant elliptic systems we establish the existence and multiplicity of solutions for some resonant elliptic systems the results are proved by applying minimax arguments and morse theory

deep ranking model by large adaptive margin learning for person re identification abstract person re identification aims to match images of the same person across disjoint camera views which is a challenging problem in video surveillance the major challenge of this task lies in how to preserve the similarity of the same person against large variations caused by complex backgrounds mutual occlusions and different illuminations while discriminating the different individuals in this paper we present a novel deep ranking model with feature learning and fusion by learning a large adaptive margin between the intra class distance and inter class distance to solve the person re identification problem specifically we organize the training images into a batch of pairwise samples treating these pairwise samples as inputs we build a novel part based deep convolutional neural network cnn to learn the layered feature representations by preserving a large adaptive margin as a result the final learned model can effectively find out the matched target to the anchor image among a number of candidates in the gallery image set by learning discriminative and stable feature representations overcoming the weaknesses of conventional fixed margin loss functions our adaptive margin loss function is more appropriate for the dynamic feature space on four benchmark datasets prid2011 market1501 cuhk01 and 3dpes we extensively conduct comparative evaluations to demonstrate the advantages of the proposed method over the state of the art approaches in person re identification

multiple solutions for semilinear elliptic equations near resonance at higher eigenvalues abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we obtain two solutions for a class of semilinear elliptic equations near resonance at higher eigenvalues

problem driven scenario generation an analytical approach for stochastic programs with tail risk measure scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program most approaches to scenario generation are distribution driven that is they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty on the other hand a problem driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty in this paper we propose an analytic approach to problem driven scenario generation this approach applies to stochastic programs where a tail risk measure such as conditional value at risk is applied to a loss function since tail risk measures only depend on the upper tail of a distribution standard methods of scenario generation which typically spread their scenarios evenly across the support of the random vector struggle to adequately represent tail risk our scenario generation approach works by targeting the construction of scenarios in areas of the distribution corresponding to the tails of the loss distributions we provide conditions under which our approach is consistent with sampling and as proof of concept demonstrate how our approach could be applied to two classes of problem namely network design and portfolio selection numerical tests on the portfolio selection problem demonstrate that our approach yields better and more stable solutions compared to standard monte carlo sampling

existence and multiplicity of nontrivial solutions for quasilinear elliptic systems abstract the existence and multiplicity of nontrivial solutions are obtained for the quasilinear elliptic systems by the linking argument the cohomological index theory and the pseudo index theory

on the mixing set with a knapsack constraint we study a substructure appearing in mixed integer programming reformulations of chance constrained programs with stochastic right hand sides over a finite discrete distribution which we call the mixing set with a knapsack constraint recently luedtke et al math program 122 2 247 272 2010 and kucukyavuz math program 132 1 31 56 2012 studied valid inequalities for such sets however most of their results were focused on the equal probabilities case when the knapsack constraint reduces to a cardinality constraint in this paper we focus on the general probabilities case general knapsack constraint we characterize the valid inequalities that do not come from the knapsack polytope and use this characterization to generalize the results previously derived for the equal probabilities case our results allow for a deep understanding of the relationship that the set under consideration has with the knapsack polytope moreover they allow us to establish benchmarks that can be used to identify when a relaxation will be useful for the considered types of reformulations of chance constrained programs

a sequential algorithm for solving nonlinear optimization problems with chance constraints an algorithm is presented for solving nonlinear optimization problems with chance constraints i e those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability in particular the algorithm is designed to solve cardinality constrained nonlinear optimization problems that arise in sample average approximations of chance constrained problems as well as in other applications in which it is only desired to enforce a minimum number of constraints the algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved the effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear ca

multi target tracking by learning local to global trajectory models the multi target tracking problem is challenging when there exist occlusions tracking failures of the detector and severe interferences between detections in this paper we propose a novel detection based tracking method that links detections into tracklets and further forms long trajectories unlike many previous hierarchical frameworks which split the data association into two separate optimization problems linking detections locally and linking tracklets globally we introduce a unified algorithm that can automatically relearn the trajectory models from the local and global information for finding the joint optimal assignment in each temporal window the trajectory models are initialized by the local information to link those easy to connect detections into a set of tracklets then the trajectory models are updated by the reliable tracklets and reused to link separated tracklets into long trajectories we iteratively update the trajectory models by more information from more frames until the result converges the iterative process gradually improves the accuracy of the trajectory models which in turn improves the target id inferences for all detections by the mrf model experiment results revealed that our proposed method achieved state of the art multi target tracking performance highlightsa unified framework to online learn local to global trajectory models is proposed the iterative algorithm can alternately update the trajectory models we solve inferences of target ids for all the detections by using the mrf model our method has low complexity compared with most state of the art methods

convex approximations of chance constrained programs we consider a chance constrained problem where one seeks to minimize a convex objective over solutions satisfying with a given close to one probability a system of randomly perturbed convex constraints this problem may happen to be computationally intractable our goal is to build its computationally tractable approximation i e an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem we construct a general class of such convex conservative approximations of the corresponding chance constrained problem moreover under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables we build a large deviation type approximation referred to as bernstein approximation of the chance constrained problem this approximation is convex and efficiently solvable we propose a simulation based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the bernstein and well known scenario approximation approaches finally we extend our construction to the case of ambiguous chance constrained problems where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly while the chance constraint should be satisfied for every distribution given by this set

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

a sample approximation approach for optimization with probabilistic constraints we study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample we show that such a sample approximation problem with a risk level larger than the required risk level will yield a lower bound to the true optimal value with probability approaching one exponentially fast this leads to an a priori estimate of the sample size required to have high confidence that the sample approximation will yield a lower bound we then provide conditions under which solving a sample approximation problem with a risk level smaller than the required risk level will yield feasible solutions to the original problem with high probability once again we obtain a priori estimates on the sample size required to obtain high confidence that the sample approximation problem will yield a feasible solution to the original problem finally we present numerical illustrations of how these results can be used to obtain feasible solutions and optimality bounds for optimization problems with probabilistic constraints

solvability for two point boundary value problems abstract suppose that h l 1 0 g c r r and lim t g t t 0 with the saddle point theorem the solvability is proved for the two point boundary value problemproblem formula under the condition that formula where formula and formula

resonance problems for the p laplacian abstract we consider resonance problems at an arbitrary eigenvalue of the p laplacian and prove the existence of weak solutions assuming a standard landesman lazer condition we use variational arguments to characterize certain eigenvalues and then to establish the solvability of the given boundary value problem

solvability of the forced duffing equation at resonance some existence theorems are obtained for periodic solutions of the forced duffing equation at resonance by the minimax methods

chance constrained problems and rare events an importance sampling approach we study chance constrained problems in which the constraints involve the probability of a rare event we discuss the relevance of such problems and show that the existing sampling based algorithms cannot be applied directly in this case since they require an impractical number of samples to yield reasonable solutions we argue that importance sampling is techniques combined with a sample average approximation saa approach can be effectively used in such situations provided that variance can be reduced uniformly with respect to the decision variables we give sufficient conditions to obtain such uniform variance reduction and prove asymptotic convergence of the combined saa is approach as it often happens with is techniques the practical performance of the proposed approach relies on exploiting the structure of the problem under study in our case we work with a telecommunications problem with bernoulli input distributions and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the is distributions although some of the results are specific to this problem we are able to draw general insights that can be useful for other classes of problems we present numerical results to illustrate our findings

strong resonance for some quasilinear elliptic equations abstract we study the existence of the weak solutions of the nonlinear boundary value problem p u 1 u p 2 u g u h x in u 0 on where the nonlinearity g is of the landesman lazer type our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue

reidentification by relative distance comparison matching people across nonoverlapping camera views at different locations and different times known as person reidentification is both a hard and important problem for associating behavior of people observed in a large distributed space over a prolonged period of time person reidentification is fundamentally challenging because of the large visual appearance changes caused by variations in view angle lighting background clutter and occlusion to address these challenges most previous approaches aim to model and extract distinctive and reliable visual features however seeking an optimal and robust similarity measure that quantifies a wide range of features against realistic viewing conditions from a distance is still an open and unsolved problem for person reidentification in this paper we formulate person reidentification as a relative distance comparison rdc learning problem in order to learn the optimal similarity measure between a pair of person images this approach avoids treating all features indiscriminately and does not assume the existence of some universally distinctive and reliable features to that end a novel relative distance comparison model is introduced the model is formulated to maximize the likelihood of a pair of true matches having a relatively smaller distance than that of a wrong match pair in a soft discriminant manner moreover in order to maintain the tractability of the model in large scale learning we further develop an ensemble rdc model extensive experiments on three publicly available benchmarking datasets are carried out to demonstrate the clear superiority of the proposed rdc models over related popular person reidentification techniques the results also show that the new rdc models are more robust against visual appearance changes and less susceptible to model overfitting compared to other related existing models