a test for linear versus convex regression function using shape restricted regression summary an unbiased test for the appropriateness of the simple linear regression model is presented the null hypothesis is that the underlying regression function is indeed a line and the alternative is that it is convex the exact distribution for a likelihood ratio test statistic is that of a mixture of beta random variables with the mixing distribution calculated from relative volumes of polyhedral convex cones determined by the convex shape restriction simulations show that the power of the test is favourable compared with the usual f test against a quadratic model for some nonquadratic choices of the underlying regression function

on large deviations in the averaging principle for sdes with a full dependence we establish the large deviation principle for stochastic differential equations with averaging in the case when all coefficients of the fast component depend on the slow one including diffusion

the geometric approach for constructing sinai ruelle bowen measures an important class of physically relevant measures for dynamical systems with hyperbolic behavior is given by sinai ruelle bowen srb measures we survey various techniques for constructing srb measures and studying their properties paying special attention to the geometric push forward approach after describing this approach in the uniformly hyperbolic setting we review recent work that extends it to non uniformly hyperbolic systems

the metastable behavior of infrequently observed weakly random one dimensional diffusion processes consider the one dimensional diffusion process x t satisfying dx t varepsilon 1 2 dw t g x t dt where w t is the standard wiener process for suitable g s with a double well at m and m shape and g m g m and for an appropriate choice of lambda varepsilon the scaled process x lambda varepsilon t converges as varepsilon to 0 in an appropriate sense to the two state m and m jump process with m an absorbing state and transitions from m to m at unit rate

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

singularities in vibro impact dynamics abstract the non differentiable nature of vibro impact dynamics can lead to breakdown of the global stable manifold theorem applicable to smooth dynamical systems in one dimensional periodically excited system the breakdown leads to the shredding of the stable manifolds and this process is analyzed in detail bodily translation of filaments of stable manifolds can lead to homoclinic intersections and this topic is discussed in the context of a new bifurcation due to re entrance shredding leads to a strong similarity between the geometries of the singular subspaces and the geometries of homoclinic tangles and strange attracting sets

on the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy we analyze the convergence of a sequential quadratic programming sqp method for nonlinear programming for the case in which the jacobian of the active constraints is rank deficient at the solution and or strict complementarity does not hold for some or any feasible lagrange multipliers we use a nondifferentiable exact penalty function and we prove that the sequence generated by an sqp using a line search is locally r linearly convergent if the matrix of the quadratic program is positive definite and constant over iterations provided that the mangasarian fromovitz constraint qualification and some second order sufficiency conditions hold

differentiable exact penalty functions for nonlinear second order cone programs we propose a method for solving nonlinear second order cone programs socps based on a continuously differentiable exact penalty function the construction of the penalty function is given by incorporating a multipliers estimate in the augmented lagrangian for socps under the nondegeneracy assumption and the strong second order sufficient condition we show that a generalized newton method has global and superlinear convergence we also present some preliminary numerical experiments

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

large deviations for a reaction diffusion equation with non gaussian perturbations in this paper we establish a large deviations principle for the non gaussian stochastic reaction diffusion equation srde partial t nu varepsilon mathscr l nu varepsilon f x nu varepsilon varepsilon sigma x nu varepsilon ddot w tx as a random perturbation of the deterministic rde partial t nu 0 mathscr l nu 0 f x nu 0 here the space variable takes values on the unit circle s 1 and mathscr l is a strongly elliptic second order operator with constant coefficients the functions f and sigma are sufficiently regular so that there is a unique solution to the above srde for any continuous initial condition we also assume that there are positive constants m and m such that m leq sigma x y leq m for all x in s 1 and all y in mathbb r the perturbation ddot w tx is the formal derivative of a brownian sheet it is known that if the initial condition is continuous then the solution will also be continuous and moreover if the initial condition is assumed to be holder continuous of exponent kappa for some 0 kappa frac 1 2 then the solution will be holder continuous of exponent kappa 2 as a function of t x in this paper we establish the large deviations principle for nu varepsilon in the holder norm of exponent kappa 2 when the initial condition is holder continuous of exponent kappa for any 0 kappa frac 1 2 and when the initial condition is assumed only to be continuous we establish the large deviations principle for nu varepsilon in the supremum norm moreover we prove that these large deviations principles are uniform with respect to the initial condition

toward a theory of rank one attractors introduction 1 statement of results part i preparation 2 relevant results from one dimension 3 tools for analyzing rank one maps part ii phase space dynamics 4 critical structure and orbits 5 properties of orbits controlled by critical set 6 identification of hyperbolic behavior formal inductive procedure 7 global geometry via monotone branches 8 completion of induction 9 construction of srb measures part iii parameter issues 10 dependence of dynamical structures on parameter 11 dynamics of curves of critical points 12 derivative growth via statistics 13 positive measure sets of good parameters appendices

averaging principle for one dimensional stochastic burgers equation abstract in this paper we consider the averaging principle for one dimensional stochastic burgers equation with slow and fast time scales under some suitable conditions we show that the slow component strongly converges to the solution of the corresponding averaged equation meanwhile when there is no noise in the slow component equation we also prove that the slow component weakly converges to the solution of the corresponding averaged equation with the order of convergence 1 r for any 0 r 1

large deviations for stochastic reaction diffusion systems with multiplicative noise and non lipshitz reaction term following classical work by freidlin trans amer math soc 1988 305 665 657 and subsequent works by sowers ann probab 1992 20 504 537 and peszat probab theory related fields 1994 98 113 136 we prove large deviation estimates for the small noise limit of systems of stochastic reaction diffusion equations with globally lipschitz but unbounded diffusion coefficients however assuming the reaction terms to be only locally lipschitz with polynomial growth this generalizes results of the above mentioned authors our results apply in particular to systems of stochastic ginzburg landau equations with multiplicative noise

an unconstrained minimization method for solving low rank sdp relaxations of the maxcut problem in this paper we consider low rank semidefinite programming lrsdp relaxations of combinatorial quadratic problems that are equivalent to the maxcut problem using the gramian representation of a positive semidefinite matrix the lrsdp problem can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function with quadratic equality constraints for the solution of this problem we propose a continuously differentiable exact merit function that exploits the special structure of the constraints and we use this function to define an efficient and globally convergent algorithm finally we test our code on an extended set of instances of the maxcut problem and we report comparisons with other existing codes

existence and stability of exact penalty for optimization problems with mixed constraints abstract in this paper we use the penalty approach in order to study minimization problems with mixed constraints in banach spaces a penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem in this paper we show that the generalized exact penalty property holds and is stable under perturbations of objective functions constraint functions and the right hand side of constraints

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

ergodic properties of the lozi mappings in this paper we construct the bowen ruelle measure for the lozi mapping an almost everywhere hyperbolic diffeomorphism of the plane we also derive some of its properties which are similar to those of an axiom a system

an algorithm for isotonic regression for two or more independent variables algorithms for solving the isotonic regression problem in more than one dimension are difficult to implement because of the large number of lower sets present or because they involve search techniques which require a significant amount of checking and readjustment here a new algorithm for solving this problem based on a simple iterative technique is proposed and shown to converge to the correct solution

slow foliation of a slow fast stochastic evolutionary system abstract this work is concerned with the dynamics of a slow fast stochastic evolutionary system quantified with a scale parameter an invariant foliation decomposes the state space into geometric regions of different dynamical regimes and thus helps understand dynamics a slow invariant foliation is established for this system it is shown that the slow foliation converges to a critical foliation i e the scale parameter is zero in probability distribution as the scale parameter tends to zero the approximation of slow foliation is also constructed with error estimate in distribution furthermore the geometric structure of the slow foliation is investigated every fiber of the slow foliation parallels each other with the slow manifold as a special fiber in fact when an arbitrarily chosen point of a fiber falls in the slow manifold the fiber must be the slow manifold itself

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

global optimum shape design abstract an optimum shape design problem can be formulated as a minimization problem of a functional subject to certain constraints usually it is nonlinear and nonconvex conventional optimization techniques are gradient based they highly depend on the initial design and are difficult to be applied to find a global solution integral global optimization algorithm is proposed to solve optimum shape design problems three design examples are given to illustrate the effectiveness of the algorithm

nonparametric quantile frontier estimation under shape restriction abstract this paper proposes a shape restricted nonparametric quantile regression to estimate the frontier which acts as a benchmark for whether a decision making unit achieves top efficiency this method adopts a two step strategy first identifying fitted values that minimize an asymmetric absolute loss under the nondecreasing and concave shape restriction second constructing a nondecreasing and concave estimator that links these fitted values this method makes no assumption on the error distribution and the functional form experimental results on some artificial data sets clearly demonstrate its superiority over the classical linear quantile regression we also discuss how to enforce constraints to avoid quantile crossings between multiple estimated frontiers with different values of finally this paper shows that this method can be applied to estimate the production function when one has some prior knowledge about the error term

large deviations for infinite dimensional stochastic dynamical systems the large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation the construction and justification of the approximations can be onerous especially in the case where the process state is infinite dimensional in this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of brownian noise the approach is based on a variational representation for functionals of brownian motion proofs of large deviations properties are reduced to demonstrating basic qualitative properties existence uniqueness and tightness of certain perturbations of the original process

a new exact exponential penalty function method and nonconvex mathematical programming abstract a new exact penalty function method called the l1 exact exponential penalty function method is introduced in this approach the so called the exponential penalized optimization problem with the l1 exact exponential penalty function is associated with the original optimization problem with both inequality and equality constraints the l1 exact exponential penalty function method is used to solve nonconvex mathematical programming problems with r invex functions with respect to the same function the equivalence between sets of optimal solutions of the original mathematical programming problem and of its associated exponential penalized optimization problem is established under suitable r invexity assumption also lower bounds on the penalty parameter are given for which above these values this result is true

sinai bowen ruelle measures for certain henon maps we study maps t a b 2 2 defined by t a b left x y right left 1 a x 2 y bx right 0 0

automatic decrease of the penalty parameter in exact penalty function methods this paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modifications to the standard outer loop which decreases the penalty parameter typically dividing it by a constant the procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the penalty parameter and is illustrated on a linear programming problem with the l1 exact penalty function and an active set approach the procedure decreases the penalty parameter when needed to the maximal value allowing the inner minimization algorithm to leave the current iterate it moreover avoids unnecessary calculations in the iteration following the step in which the penalty parameter is decreased we report on preliminary computational results which show that this method can require fewer iterations than the standard way to update the penalty parameter this approach permits a better understanding of the performance of exact penalty methods

existence of approximate exact penalty in constrained optimization in this paper we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish the exact penalty property for a large class of inequality constrained minimization problems

an augmented lagrangian function with improved exactness properties in this paper we introduce a new exact augmented lagrangian function for the solution of general nonlinear programming problems for this lagrangian function a complete equivalence between its unconstrained minimization on an open set and the solution of the original constrained problem can be established under mild assumptions and without requiring the boundedness of the feasible set of the constrained problem moreover we describe an unconstrained algorithmic model which is globally convergent toward kkt pairs of the original constrained problem the algorithmic model can be endowed with a superlinear rate of convergence by a proper choice of the search direction in the unconstrained minimization without requiring strict complementarity

exact penalty functions method for mathematical programming problems involving invex functions in this paper some new results on the exact penalty function method are presented simple optimality characterizations are given for the differentiable nonconvex optimization problems with both inequality and equality constraints via exact penalty function method the equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable invexity assumption furthermore the equivalence between a saddle point in the invex mathematical programming problem and an optimal point in its exact penalized optimization problem is also proved

large deviations and approximations for slow fast stochastic reaction diffusion equations abstract a large deviation principle is derived for a class of stochastic reaction diffusion partial differential equations with slow fast components the result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small gaussian perturbation this result also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow fast stochastic partial differential equations

on some properties of quadratic programs with a convex quadratic constraint in this paper we consider the problem of minimizing a possibly nonconvex quadratic function with a quadratic constraint we point out some new properties of the problem in particular in the first part of the paper we show that i given a kkt point that is not a global minimizer it is easy to find a better feasible point ii strict complementarity holds at the local nonglobal minimizer in the second part of this paper we show that the original constrained problem is equivalent to the unconstrained minimization of a piecewise quartic merit function using the unconstrained formulation we give in the nonconvex case a new second order necessary condition for global minimizers in the third part of this paper algorithmic applications of the preceding results are briefly outlined and some preliminary numerical experiments are reported

scalable nonlinear programming via exact differentiable penalty functions and trust region newton methods we present an approach for nonlinear programming based on the direct minimization of an exact differentiable penalty function using trust region newton techniques the approach provides desirable features required for scalability it can detect and exploit directions of negative curvature it is superlinearly convergent and it enables the scalable computation of the newton step through iterative linear algebra moreover it presents features that are desirable for parametric optimization problems that must be solved in a latency limited environment as is the case for model predictive control and mixed integer nonlinear programming these features are fast detection of activity efficient warm starting and progress on a primal dual merit function at every iteration we note that other algorithmic approaches fail to satisfy at least one of these features we derive general convergence results for our approach and demonstrate its behavior through numerical studies

local analysis of a new multipliers method abstract in this paper we introduce a penalty function and a corresponding multipliers method for the solution of a class of nonlinear programming problems where the equality constraints have a particular structure the class models optimal control and engineering design problems with bounds on the state and control variables and has wide applicability the multipliers method updates multipliers corresponding to inequality constraints maintaining their nonnegativity instead of dealing with multipliers associated with equality constraints the basic local convergence properties of the method are proved and a dual framework is introduced we also analyze the properties of the penalized problem related with the penalty function

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

averaging principle for a class of stochastic reaction diffusion equations we consider the averaging principle for stochastic reaction diffusion equations under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component we calculate limiting slow motion the study of solvability of kolmogorov equations in hilbert spaces and the analysis of regularity properties of solutions allow to generalize the classical approach to finite dimensional problems of this type in the case of spde s

large deviations for a class of stochastic partial differential equations we consider the random fields x e t q t 0 q o governed by stochastic partial differential equations driven by a gaussian white noise in space time where o is a bounded domain in lid with regular boundary to study the continuity of the random fields x e in space and time variables we prove an analogue of garsia s theorem we then derive the large deviation results based on the methods used by the second author in another paper this article provides an alternative proof of sowers result for the case of d 1

the vector exact l1 penalty method for nondifferentiable convex multiobjective programming problems abstract in this paper the vector exact l 1 penalty function method for nondifferentiable convex multiobjective programming problems is analyzed the vector penalized optimization problem with the vector exact l 1 penalty function is defined conditions are given guaranteeing the equivalence of the sets of weak pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l 1 penalty function this equivalence is established for nondifferentiable vector optimization problems with convex functions

large deviation principle for stochastic evolution equations the large deviation principle obtained by freidlin and wentzell for measures associated with finite dimensional diffusions is extended to measures given by stochastic evolution equations with non additive random perturbations the proof of the main result is adopted from the priouret paper concerning finite dimensional diffusions exponential tail estimates for infinite dimensional stochastic convolutions are used as main tools

large deviation problem for some parabolic itǒ equations the large deviation problem of wentzell freidlin type is considered for a class of semilinear parabolic equations perturbed by a small multiplicative noise in a hilbert space setting it is proved that under suitable conditions the associated family of solution measures depending on a small parameter obeys the large deviation principle with respect to a certain rate function

global minimization of constrained problems with discontinuous penalty functions abstract with the integral approach to global optimization a class of discontinuous penalty functions is proposed to solve constrained minimization problems optimality conditions of a penalized minimization problem are generalized to a discontinuous case necessary and sufficient conditions for an exact penalty function are examined a nonsequential algorithm is proposed numerical examples are given to illustrate the effectiveness of the algorithm

exact penalty property in optimization with mixed constraints via variational analysis in this paper we use the penalty approach in order to study constrained minimization problems in infinite dimensional asplund spaces with nonsmooth nonconvex mixed constraints a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish sufficient conditions for the exact penalty properties using the notion of the mordukhovich basic subdifferential

convergence to second order stationary points in inequality constrained optimization we propose a new algorithm for the nonlinear inequality constrained minimization problem and prove that it generates a sequence converging to points satisfying the kkt second order necessary conditions for optimality the algorithm is a line search algorithm using directions of negative curvature and it can be viewed as a nontrivial extension of corresponding known techniques from unconstrained to constrained problems the main tools employed in the definition and in the analysis of the algorithm are a differentiable exact penalty function and results from the theory of lc1 functions

a nonmonotone filter sqp method local convergence and numerical results the work by gould loh and robinson siam j optim 24 2014 pp 175 209 established global convergence of a new filter line search method for finding local first order solutions to nonlinear and nonconvex constrained optimization problems a key contribution of that work was that the search direction was computed using the same procedure during every iteration from subproblems that were always feasible and computationally tractable this contrasts previous filter methods that require a separate restoration phase based on subproblems solely designed to reduce infeasibility in this paper we present a nonmonotone variant of our previous algorithm that inherits the previously established global convergence property in addition we establish local superlinear convergence of the iterates and provide the results of numerical experiments the numerical tests validate our method and highlight an interesting numerical trade off between accepting more on average lower quality steps versus fewer on avera

an algorithm for restricted least squares regression abstract a commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints here a simple iterative algorithm is presented and shown to converge to the desired solution several examples are presented including finding the closest concave convex function to a set of points and other general quadratic programming problems the dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm finally extensions to expressions other than least squares are given

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

existence of exact penalty for constrained optimization problems in hilbert spaces in this paper we use the penalty approach in order to study constrained minimization problems in a complete metric space with locally lipschitzian mixed constraints a penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem in this paper we establish sufficient conditions for the exact penalty property

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

the exact penalty principle abstract the exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem most results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem and the reverse property is rarely studied in this paper we study the reverse property we give the conditions under which the original constrained single and or multiobjective optimization problem and the unconstrained exact penalized problem are exactly equivalent the main conditions to ensure the exact penalty principle for optimization problems include the global and local error bound conditions by using variational analysis these conditions may be characterized by using generalized differentiation

average and deviation for slow fast stochastic partial differential equations abstract averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes this article derives an averaged equation for a class of stochastic partial differential equations without any lipschitz assumption on the slow modes the rate of convergence in probability is obtained as a byproduct importantly the stochastic deviation between the original equation and the averaged equation is also studied a martingale approach proves that the deviation is described by a gaussian process this gives an approximation to errors of order o instead of order o attained in previous averaging

stochastic non convex envelopment of data applying isotonic regression to frontier estimation abstract isotonic nonparametric least squares inls is a regression method for estimating a monotonic function by fitting a step function to data in the literature of frontier estimation the free disposal hull fdh method is similarly based on the minimal assumption of monotonicity in this paper we link these two separately developed nonparametric methods by showing that fdh is a sign constrained variant of inls we also discuss the connections to related methods such as data envelopment analysis dea and convex nonparametric least squares cnls further we examine alternative ways of applying isotonic regression to frontier estimation analogous to corrected and modified ordinary least squares cols mols methods known in the parametric stream of frontier literature we find that inls is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings in the absence of noise the corrected inls cinls has a higher discriminating power than fdh in the case of noisy data we propose to apply the method of non convex stochastic envelopment of data non convex stoned which disentangles inefficiency from noise based on the skewness of the inls residuals the proposed methods are illustrated by means of simulated examples

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v

a penalty method for american options with jump diffusion processes the fair price for an american option where the underlying asset follows a jump diffusion process can be formulated as a partial integral differential linear complementarity problem we develop an implicit discretization method for pricing such american options the jump diffusion correlation integral term is computed using an iterative method coupled with an fft while the american constraint is imposed by using a penalty method we derive sufficient conditions for global convergence of the discrete penalized equations at each timestep finally we present numerical tests which illustrate such convergence

using svm to combine global heuristics for the standard quadratic problem abstract the standard quadratic problem stqp is an np hard problem with many local minimizers stationary points in the literature heuristics based on unconstrained continuous non convex formulations have been proposed bomze palagi 2005 bomze grippo palagi 2012 but none dominates the other in terms of best value found following cassioli dilorenzo locatelli schoen sciandrone 2012 we propose to use support vector machines svms to define a multistart global strategy which selects the best heuristic we test our method on stqp arising from the maximum clique problem on a graph which is a challenging combinatorial problem we use as benchmark the clique problems in the dimacs challenge