globally and superlinearly convergent algorithm for minimizing a normal merit function in this paper we present two new concepts related to the solution of systems of nonsmooth equations ne and variational inequalities vi the first concept is that of a normal merit function which summarizes the simple basic properties shared by various known merit functions in general normal merit functions are locally lipschitz but not differentiable the second concept is that of a newtonian operator whose values generalize the concept of the hessian for normal merit functions these two concepts are then used to generalize the nonsmooth newton method for solving the equation nabla f x 0 where f is a normal merit function with f in c 1 to the case where f is only locally lipschitz and the set valued inclusion 0 in partial f x needs to be solved combining the resulting generalized newton method with certain first order methods we obtain a globally and superlinearly convergent algorithm for minimizing normal merit functions

a semismooth equation approach to the solution of nonlinear complementarity problems in this paper we present a new algorithm for the solution of nonlinear complementarity problems the algorithm is based on a semismooth equation reformulation of the complementarity problem we exploit the recent extension of newton s method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions other interesting features of the new algorithm are an extreme simplicity along with a low computational burden per iteration we include numerical tests which show the viability of the approach

a fast convergent sequential linear equation method for inequality constrained optimization without strict complementarity abstract in this paper a type of smooth nonlinear optimization problems with inequality constraints is considered and a new sequential linear equation algorithm is proposed by introducing a new constructing technique for the system of linear equations sle which depends on the perturbation of the constraints gradients at each iteration of the proposed algorithm one or more sles need to be solved specially only one sle is required to be solved when the iterates are sufficiently close to the solution i e after a finite number of iterations which decreases the amount of computations the search technique is a combination of the line armijo type and newton step size under mild assumptions without the strict complementarity it is shown that the proposed algorithm enjoys the properties of global and superlinear convergence finally some preliminary numerical tests are reported and the numerical results show that the proposed algorithm is promising

covering of a finite lattice by a random walk abstract we study the covering process by a simple random walk of a d dimensional periodic hypercubic lattice of n sites in d 1 the probability l n x for site x to be the last site visited in this covering process does not depend on x as long as x is not the starting point of the walk we argue that in dimensions d 2 the probability l n x approaches a constant value according to a coulomb law l n x 1 2 1 const x d 2 valid for x small on the scale n 1 d whereas it behaves logarithmically in d 2 also there is a dimension dependent characteristic time scale on which the last site is visited the structure of the set of sites not yet visited on this characteristic time scale is fractal like in d 2 in d 3 on the other hand this set is essentially distributed randomly through the lattice

on the constant positive linear dependence condition and its application to sqp methods in this paper we introduce a constant positive linear dependence condition cpld which is weaker than the mangasarian fromovitz constraint qualification mfcq and the constant rank constraint qualification crcq we show that a limit point of a sequence of approximating karush kuhn tucker kkt points is a kkt point if the cpld holds there we show that a kkt point satisfying the cpld and the strong second order sufficiency conditions ssosc is an isolated kkt point we then establish convergence of a general sequential quadratical programming sqp method under the cpld and the ssosc finally we apply these results to analyze the feasible sqp method proposed by panier and tits in 1993 for inequality constrained optimization problems we establish its global convergence under the ssosc and a condition slightly weaker than the mangasarian fromovitz constraint qualification and we prove superlinear convergence of a modified version of this algorithm under the ssosc and a condition slightly weaker than the linear independence constraint qualification

new active set identification for general constrained optimization and minimax problems abstract the purpose of this paper is to discuss the problem of identifying the active constraints for general constrained nonlinear programming and constrained minimax problems at an isolated local solution facchinei fischer and kanzow 4 proposed an effective technique which can identify the active set in a neighborhood of an isolated local solution for nonlinear programming and han jian and li 5 improved and extended this to minimax problems in this work a new active constraint identification set is constructed not only is it tighter than the previous two identification sets but also it can be used effectively in penalty algorithms without strict complementarity and linear independence it is shown that the new identification technique can accurately identify the active constraints of nonlinear programming and constrained minimax problems some numerical examples illustrate the identification technique

coalescing random walks and voter model consensus times on the torus in mathbb z d voter models on z d and on the torus of site n in z d are considered the second ones get trapped with probability 1 as t tends to infinity at all 0 s or all 1 s the asymptotic growth of these trapping times are examined as n tends to infinity this is done with limit thewems for coalescing random walk systems on the torus of side n in z d

modified newton methods for solving a semismooth reformulation of monotone complementarity problems in this paper we propose a newton type method for solving a semismooth reformulation of monotone complementarity problems in this method a direction finding subproblem which is a system of linear equations is uniquely solvable at each iteration moreover the obtained search direction always affords a direction of sufficient decrease for the merit function defined as the squared residual for the semismooth equation equivalent to the complementarity problem we show that the algorithm is globally convergent under some mild assumptions next by slightly modifying the direction finding problem we propose another newton type method which may be considered a restricted version of the first algorithm we show that this algorithm has a superlinear or possibly quadratic rate of convergence under suitable assumptions finally some numerical results are presented

a new qp free globally convergent locally superlinearly convergent algorithm for inequality constrained optimization in this paper we propose a new qp free method which ensures the feasibility of all iterates for inequality constrained optimization the method is based on a nonsmooth equation reformulation of the kkt optimality condition by using the fischer burmeister nonlinear complementarity problem function the study is strongly motivated by recent successful applications of this function to the complementarity problem and the variational inequality problem the method we propose here enjoys some advantages over similar methods based on the equality part of the kkt optimality condition for example without assuming isolatedness of the accumulation point or boundedness of the lagrangian multiplier approximation sequence we show that every accumulation point of the iterative sequence generated by this method is a kkt point if the linear independence condition holds and if the second order sufficient condition and the strict complementarity condition hold the method is superlinearly convergent some preliminary numerical results indicate that this new qp free method is quite promising

semismooth karush kuhn tucker equations and convergence analysis of newton and quasi newton methods for solving these equations there are several forms of systems of nonsmooth equations which are equivalent to the karush kuhn tucker kkt system of a nonlinearly constrained optimization problem nlp if the nlp is twice continuously differentiable and the hessian functions of its objective and constraint functions are locally lipschitzian then these kkt equations are strongly semismooth if furthermore the linear independence condition and the strong second order sufficiency condition are satisfied at a kkt point then the generalized jacobians of these kkt equations are nonsingular at that point and the sequence generated by the generalized newton method converges to this point q quadratically however direct application of quasi newton methods cannot guarantee q superlinear convergence we present a mixed quasi newton method which converges q superlinearly with common symmetrical updating rules under the above conditions for the generalized newton method superlinear convergence of the primal variables and global convergence are also discussed

a filter active set algorithm for ball sphere constrained optimization problem in this paper we propose a filter active set algorithm for the minimization problem over a product of multiple ball sphere constraints by making effective use of the special structure of the ball sphere constraints a new limited memory bfgs l bfgs scheme is presented the new l bfgs implementation takes advantage of the sparse structure of the jacobian of the constraints and generates curvature information of the minimization problem at each iteration only two or three reduced linear systems are required to solve for the search direction the filter technique combined with the backtracking line search strategy ensures the global convergence and the local superlinear convergence can also be established under mild conditions the algorithm is applied to two specific applications the nearest correlation matrix with factor structure and the maximal correlation problem our numerical experiments indicate that the proposed algorithm is competitive with some recently custom designed methods for each ind

a qp free algorithm without a penalty function or a filter for nonlinear general constrained optimization abstract in this paper we present a qp free algorithm without a penalty function or a filter for nonlinear general constrained optimization at each iteration three systems of linear equations with the same coefficient matrix are solved to yield search direction the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced there is no feasibility restoration phase in our algorithm which is necessary for filter methods the algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness finally some preliminary numerical results are reported

random walks on lattices with points of two colors ii some rigorous inequalities for symmetric random walks we continue our investigation of a model of random walks on lattices with two kinds of points black and white the colors of the points are stochastic variables with a translation invariant but otherwise arbitrary joint probability distribution the steps of the random walk are independent of the colors we are interested in the stochastic properties of the sequence of consecutive colors encountered by the walker in this paper we first summarize and extend our earlier general results then under the restriction that the random walk be symmetric we derive a set of rigorous inequalities for the average length of the subwalk from the starting point to a first black point and of the subwalks between black points visited in succession a remarkable difference in behavior is found between subwalks following an odd numbered and subwalks following an evennumbered visit to a black point the results can be applied to a trapping problem by identifying the black points with imperfect traps

feasible methods for nonconvex nonsmooth problems with applications in green communications we propose a general feasible method for nonsmooth nonconvex constrained optimization problems the algorithm is based on the inexact solution of a sequence of strongly convex optimization subproblems followed by a step size procedure key features of the scheme are i it preserves feasibility of the iterates for nonconvex problems with nonconvex constraints ii it can handle nonsmooth problems and iii it naturally leads to parallel distributed implementations we illustrate the application of the method to an open problem in green communications whereby the energy consumption in mimo multiuser interference networks is minimized subject to nonconvex quality of service constraints

the use of qp free algorithm in the limit analysis of slope stability in many mountainous areas landslides and slope instabilities frequently occur after heavy rainfall and earthquake and result in enormous casualties and huge economic losses in order to mitigate the landslides hazard efficiently a method is required for a better understanding of stability analysis fortunately upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes and in this approach the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization in general the sqp type algorithms are used to solve this optimization problem however it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the sqp type algorithms fortunately a qp free algorithm based on penalty function and active set strategy can be globally convergent toward the kkt points with arbitrary starting point and the rate of convergence is local superlinear or even quadratic two classical problems of slope stability are solved by this qp free algorithm the results show that the qp free algorithm would be the better choice than sqp type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability

a robust sequential quadratic programming method the sequential quadratic programming method developed by wilson han and powell may fail if the quadratic programming subproblems become infeasible or if the associated sequence of search directions is unbounded this paper considers techniques which circumvent these difficulties by modifying the structure of the constraint region in the quadratic programming subproblems furthermore questions concerning the occurrence of an unbounded sequence of multipliers and problem feasibility are also addressed

random walks on lattices with randomly distributed traps i the average number of steps until trapping for a random walk on a lattice with a random distribution of traps we derive an asymptotic expansion valid for smallq for the average number of steps until trapping whereq is the probability that a lattice point is a trap we study the case of perfect traps where the walk comes to an end and the extension obtained by letting the traps be imperfect i e by giving the walker a finite probability to remain free when stepping on a trap several classes of random walks of varying dimensionality are considered and special care is taken to show that the expansion derived is exact up to and including the last term calculated the numerical accuracy of the expansion is discussed

a modified sqp algorithm for minimax problems in this paper a modified nonmonotone line search sqp algorithm for nonlinear minimax problems is presented during each iteration of the proposed algorithm a main search direction is obtained by solving a reduced quadratic program qp in order to avoid the maratos effect a correction direction is generated by solving the reduced system of linear equations under mild conditions the global and superlinear convergence can be achieved finally some preliminary numerical results are reported

on the accurate identification of active set for constrained minimax problems abstract in this paper the problem of identifying the active constraints for constrained nonlinear programming and minimax problems at an isolated local solution is discussed the correct identification of active constraints can improve the local convergence behavior of algorithms and considerably simplify algorithms for inequality constrained problems so it is a useful adjunct to nonlinear optimization algorithms facchinei et al f facchinei a fischer c kanzow on the accurate identification of active constraints siam j optim 9 1998 14 32 introduced an effective technique which can identify the active set in a neighborhood of a solution for nonlinear programming in this paper we first improve this conclusion to be more suitable for infeasible algorithms such as the strongly sub feasible direction method and the penalty function method then we present the identification technique of active constraints for constrained minimax problems without strict complementarity and linear independence some numerical results illustrating the identification technique are reported

a new superlinearly convergent norm relaxed method of strongly sub feasible direction for inequality constrained optimization method of feasible directions mfd is an important method for solving nonlinearly constrained optimization however various types of mfd all need an initial feasible point which can not be found easily in generally in addition the computational cost of some mfd with superlinearly convergent property is rather high on the other hand the strongly sub feasible direction method does not need an initial feasible point but most of the proposed algorithm do not have the superlinearly convergent property and can not guarantee that the iteration point is feasible after finite iterations in this paper we present a new superlinearly convergent algorithm with arbitrary initial point at each iteration a master direction is obtained by solving one direction finding subproblem dfs and an auxiliary direction is yielded by an explicit formula after finite iterations the iteration point goes into the feasible set and the master direction is a feasible direction of descent since a new generalized projection technique is contained in the auxiliary direction formula under some mild assumptions without the strict complementarity the global convergence and superlinear convergence of the algorithm can be obtained

electric field and potential calculation for a bioelectric current dipole in an ellipsoid computer based modelling in ellipsoidal geometry can be useful in electro encephalography and gastrography due to the resemblance of the human brain and stomach to an ellipsoid both theoretically and computationally the bioelectric current dipole model is important for the study of electrical activity in these two organs computing the electric potential and electric field e due to a current dipole located in an ellipsoid requires truncated series expansions involving ellipsoidal harmonics which are the products of lame functions a theoretical model for this has appeared in the literature only for expansions of order 2 in however this may be insufficient in forward electrogastrography while an analogous situation is encountered in some geodetic problems where similar expansions are required in this paper we propose a generalized model for computing and e numerically using harmonic expansions of arbitrary order and degree the implementation of such a procedure involves finding roots of lame polynomials of degree 5 or higher using an optimization technique for solving nonlinear systems of equations this process can allow one to make a knowledgeable decision concerning the optimal expansion size required for the physical problem under investigation without compromising the overall accuracy of the computation

a generalized super memory gradient projection method of strongly sub feasible directions with strong convergence for nonlinear inequality constrained optimization in this work combining the properties of the generalized super memory gradient projection methods with the ideas of the strongly sub feasible directions methods we present a new algorithm with strong convergence for nonlinear inequality constrained optimization at each iteration the proposed algorithm can sufficiently use the information of the previous t steps iterations to generate a new iterative point particularly the intervals of parameters in the super memory gradient projection direction are adjustable the main properties of the new algorithm are described as follows i the improving super memory gradient projection direction is a combination of the generalized gradient projection and the t steps super memory gradients which include both the previous t steps search directions and gradients moreover only the gradients associated with a generalized active constrained set are dealt with rather than the gradients of all constraints ii the initial point can be chosen arbitrarily and at each iteration the number of the functions satisfying the inequality constraints is nondecreasing especially once a feasible iteration is obtained then the subsequent iterations are also feasible iii under suitable assumptions it possesses global and strong convergence finally some preliminary numerical results show that the proposed algorithm is promising

modified wilson s method for nonlinear programswith nonunique multipliers this paper first investigates newton type methods for generalized equations with compact solution sets the analysis of their local convergence behavior is based besides other conditions on the upper lipschitz continuity of the local solution set mapping of a simply perturbed generalized equation this approach is then applied to the kkt conditions of a nonlinear program with inequality constraints and leads to a modified version of the classical wilson method it is shown that the distances of the iterates to the set of kkt points converge q quadratically to zero under conditions that do not imply a unique multiplier vector additionally to the mangasarian fromovitz constraint qualification and to a second order sufficiency condition the local minimizer is required to fulfill a constant rank condition weaker than the constant rank constraint qualification one of janin and a so called weak complementarity condition

superlinearly convergent approximate newton methods for lc 1 optimization problems in the literature the proof of superlinear convergence of approximate newton or sqp methods for solving nonlinear programming problems requires twice smoothness of the objective and constraint functions sometimes the second order derivatives of those functions are required to be lipschitzian in this paper we present approximate newton or sqp methods for solving nonlinear programming problems whose objective and constraint functions have locally lipschitzian derivatives and establishq superlinear convergence of these methods under the assumption that these derivatives are semismooth this assumption is weaker than the second order differentiability the extended linear quadratic programming problem in the fully quadratic case is an example of nonlinear programming problems whose objective functions have semismooth but not smooth derivatives

magnetoencephalography in ellipsoidal geometry an exact analytic solution for the forward problem in the theory of biomagnetics of the human brain is known only for the 1d case of a sphere and the 2d case of a spheroid where the excitation field is due to an electric dipole within the corresponding homogeneous conductor in the present work the corresponding problem for the more realistic ellipsoidal brain model is solved and the leading quadrupole approximation for the exterior magnetic field is obtained in a form that exhibits the anisotropic character of the ellipsoidal geometry the results are obtained in a straightforward manner through the evaluation of the interior electric potential and a subsequent calculation of the surface integral over the ellipsoid using lame functions and ellipsoidal harmonics the basic formulas are expressed in terms of the standard elliptic integrals that enter the expressions for the exterior lame functions the laborious task of reducing the results to the spherical geometry is also included

on combining feasibility descent and superlinear convergence in inequality constrained optimization extension of quasi newton techniques from unconstrained to constrained optimization via sequential quadratic programming sqp presents several difficulties among these are the possible inconsistency away from the solution of first order approximations to the constraints resulting in infeasibility of the quadratic programs and the task of selecting a suitable merit function to induce global convergence in ths case of inequality constrained optimization both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints and that yield monotonically decreasing objective function values feasibility of the successive iterates is in fact required in many contexts such as in real time applications or when the objective function is not well defined outside the feasible set it has been recently shown that this can be achieved while preserving local two step superlinear convergence in this note the essential ingredients for an sqp based method exhibiting the desired properties are highlighted correspondingly a class of such algorithms is described and analyzed tests performed with an efficient implementation are discussed

a kind of qp free feasible method this paper is concerned with a kind of qp free feasible algorithm which solves an inequality constrained nonlinear optimization problem under some weaker conditions than those in h qi l qi a new qp free globally convergent locally superlinear convergent algorithm for inequality constrained optimization siam j optim 11 2000 113 132 we prove that the algorithm is implementable and globally convergent moreover some numerical test results are given to indicate that the algorithm is quite promising

piecewise smoothness local invertibility and parametric analysis of normal maps this paper is concerned with properties of the euclidean projection map onto a convex set defined by finitely many smooth convex inequalities and affine equalities under a constant rank constraint qualification we show that the projection map is piecewise smooth pc1 hence bouligand differentiable or directionally differentiable and a relatively simple formula is given for the b derivative these properties of the projection map are used to obtain inverse and implicit function theorems for associated normal maps using a new characterization of invertibility of a pc1 function in terms of its b derivative an extension of the implicit function theorem which does not require local uniqueness is also presented degree theory plays a major role in the analysis of both the locally unique case and its extension

a feasible qp free algorithm combining the interior point method with active set for constrained optimization in this paper by means of working set technique for determining the active set and the idea of primal dual interior point method a new feasible qp free algorithm for solving inequality constrained optimization problems is presented at each iteration the algorithm solves only three reduced systems of linear equations with common coefficient matrix moreover the initial iteration point can be at constraint boundary and the coefficient matrix is uniformly nonsingular without the strict complementarity we also prove that the proposed algorithm obtains global and superlinear convergence at last preliminary numerical results are reported

electroencephalography in ellipsoidal geometry the human brain is shaped in the form of an ellipsoid with average semiaxes equal to 6 6 5 and 9 cm this is a genuine 3 d shape that reflects the anisotropic characteristics of the brain as a conductive body the direct electroencephalography problem in such anisotropic geometry is studied in the present work the results which are obtained through successively solving an interior and an exterior boundary value problem are expressed in terms of elliptic integrals and ellipsoidal harmonics both in jacobian as well as in cartesian form reduction of our results to spheroidal as well as to spherical geometry is included in contrast to the spherical case where the boundary does not appear in the solution the boundary of the realistic conductive brain enters explicitly in the relative expressions for the electric field moreover the results in all three geometrical models reveal that to some extend the strength of the electric source is more important than its location

the revised dfp algorithm without exact line search in this paper we discuss the convergence of the dfp algorithm with revised search direction under some inexact line searches we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of the algorithm is one step superlinear and n step second order for uniformly convex objective functions from the proof of this paper we obtain the superlinear and n step second order convergence of the dfp algorithm for uniformly convex objective functions

combinatorial formulae for the derivatives of lame functions lame functions play a central role in the theory of ellipsoidal harmonics and have many varied applications in mathematical physics in this article a generalized approach to the computation of lame function derivatives of arbitrary order is derived and it is demonstrated how these derivatives can be expressed recursively in terms of the original lame functions by making use of combinatorial formulae discovered by di bruno girard and waring

a feasible sequential linear equation method for inequality constrained optimization in this paper by means of the concept of the working set which is an estimate of the active set we propose a feasible sequential linear equation algorithm for solving inequality constrained optimization problems at each iteration of the proposed algorithm we first solve one system of linear equations with a coefficient matrix of size m m where m is the number of constraints to compute the working set we then solve a subproblem which consists of four reduced systems of linear equations with a common coefficient matrix unlike existing qp free algorithms the subproblem is concerned with only the constraints corresponding to the working set the constraints not in the working set are neglected consequently the dimension of each subproblem is not of full dimension without assuming the isolatedness of the stationary points we prove that every accumulation point of the sequence generated by the proposed algorithm is a kkt point of the problem moreover after finitely many iterations the working set becomes independent of the iterates and is essentially the same as the active set of the kkt point in other words after finitely many steps only those constraints which are active at the solution will be involved in the subproblem under some additional conditions we show that the convergence rate is two step superlinear or even q superlinear we also report some preliminary numerical experiments to show that the proposed algorithm is practicable and effective for the test problems

feasible descent algorithms for mixed complementarity problems in this paper we consider a general algorithmic framework for solving nonlinear mixed complementarity problems the main features of this framework are a it is well defined for an arbitrary mixed complementarity problem b it generates only feasible iterates c it has a strong global convergence theory and d it is locally fast convergent under standard regularity assumptions this framework is applied to the path solver in order to show viability of the approach numerical results for an appropriate modification of the path solver indicate that this framework leads to substantial computational improvements

a superlinearly convergent qp free algorithm for mathematical programs with equilibrium constraints in this paper based on the smoothing techniques and the working set techniques a qp free algorithm for mathematical programs with equilibrium constraints mpec for short is presented firstly by fischer burmeister function and smoothing techniques the discussed problem is approximated by a smooth constrained optimization problem secondly the working set which is used to construct systems of linear equations is generated by pivoting operation at each iteration the search direction is yielded by solving two or three systems of equations with the same coefficient matrix under mild conditions the global convergence and superlinear convergence are shown moreover we can conclude that the current iterative point is an exact stationary point of the discussed problem if the proposed algorithm stops after finite iterations finally preliminary numerical results are reported

newton s method for quadratic stochastic programs with recourse abstract quadratic stochastic programs qsp with recourse can be formulated as nonlinear convex programming problems by attaching a lagrange multiplier vector to the nonlinear convex program a qsp is written as a system of nonsmooth equations a newton like method for solving the qsp is proposed and global convergence and local super linear convergence of the method are established the current method is more general than previous methods which were developed for box diagonal and fully quadratic qsp numerical experiments are given to demonstrate the efficiency of the algorithm and to compare the use of monte carlo rules and lattice rules for multiple integration in the algorithm

a superlinearly convergent feasible method for the solution of inequality constrained optimization problems when iteratively solving optimization problems arising from engineering design applications it is sometimes crucial that all iterates satisfy a given set of hard inequality constraints and generally desirable that the objective function value improve at each iteration in this paper we propose an algorithm of the successive quadratic programming sqp type which unlike other algorithms of this type does enjoy such properties under mild assumptions the new algorithm is shown to converge from any initial point locally superlinearly numerically tested it has proven to be competitive with the most successful currently available nonlinear programming algorithms while the latter do not exhibit the desired properties

statistical properties of the set of sites visited by the two dimensional random walk we study the support i e the set of visited sites of a t step random walk on a two dimensional square lattice in the large t limit a broad class of global properties m t of the support is considered including for example the number s t of its sites the length of its boundary the number of islands of unvisited sites that it encloses the number of such islands of given shape size and orientation and the number of occurrences in space of specific local patterns of visited and unvisited sites on a finite lattice we determine the scaling functions that describe the averages on appropriate lattice size dependent time scales on an infinite lattice we first observe that the all increase with t as where k is an m dependent positive integer we then consider the class of random processes constituted by the fluctuations around average we show that to leading order as t gets large these fluctuations are all proportional to a single universal random process normalized to for the probability law of tends to that of varadhan s renormalized local time of self intersections an implication is that in the long time limit all are proportional to

a two stage feasible directions algorithm for nonlinear constrained optimization we present a feasible directions algorithm based on lagrangian concepts for the solution of the nonlinear programming problem with equality and inequality constraints at each iteration a descent direction is defined by modifying it we obtain a feasible descent direction the line search procedure assures the global convergence of the method and the feasibility of all the iterates we prove the global convergence of the algorithm and apply it to the solution of some test problems although the present version of the algorithm does not include any second order information like quasi newton methods these numerical results exhibit a behavior comparable to that of the best methods known at present for nonlinear programming

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

a superlinearly convergent strongly sub feasible ssle type algorithm with working set for nonlinearly constrained optimization in this paper by means of a new efficient identification technique of active constraints and the method of strongly sub feasible direction we propose a new sequential system of linear equations ssle algorithm for solving inequality constrained optimization problems in which the initial point is arbitrary at each iteration we first yield the working set by a pivoting operation and a generalized projection then three or four reduced linear equations with a same coefficient are solved to obtain the search direction after a finite number of iterations the algorithm can produced a feasible iteration point and it becomes the method of feasible directions moreover after finitely many iterations the working set becomes independent of the iterates and is essentially the same as the active set of the kkt point under some mild conditions the proposed algorithm is proved to be globally strongly and superlinearly convergent finally some preliminary numerical experiments are reported to show that the algorithm is practicable and effective

on the accurate identification of active constraints we consider nonlinear programs with inequality constraints and we focus on the problem of identifying those constraints which will be active at an isolated local solution the correct identification of active constraints is important from both a theoretical and a practical point of view such an identification removes the combinatorial aspect of the problem and locally reduces the inequality constrained minimization problem to an equality constrained problem which can be more easily dealt with we present a new technique which identifies active constraints in a neighborhood of a solution and which requires neither complementary slackness nor uniqueness of the multipliers we also present extensions to variational inequalities and numerical examples illustrating the identification technique

convergence of the bfgs method for lc 1 convex constrained optimization this paper proposes a bfgs sqp method for linearly constrained optimization where the objective function f is required only to have a lipschitz gradient the karush kuhn tucker system of the problem is equivalent to a system of nonsmooth equations f v 0 at every step a quasi newton matrix is updated if f v k satisfies a rule this method converges globally and the rate of convergence is superlinear when f is twice strongly differentiable at a solution of the optimization problem no assumptions on the constraints are required this generalizes the classical convergence theory of the bfgs method which requires a twice continuous differentiability assumption on the objective function applications to stochastic programs with recourse on a cm5 parallel computer are discussed

random walks on lattices with points of two colours i abstract this paper is concerned with random walks on lattices with two kinds of points black and white the colours of the points are random variables with a translation invariant but otherwise arbitrary joint probability distribution the steps of the walk are independent of the colours we study the stochastic properties of the length of the subwalk from the starting point to a first black point and of subwalks between points visited in succession and establish a number of exact relations these relations can be applied to a trapping problem by identifying the black points with imperfect traps an example is discussed

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

random walks with spontaneous emission on lattices with periodically distributed imperfect traps abstract we study random walks on d dimensional lattices with periodically distributed traps in which the walker has a finite probability per step of disappearing from the lattice and a finite probability of escaping from a trap general expressions are derived for the total probability that the walk ends in a trap and for the moments of the number of steps made before this happens if it does happen the analysis is extended to lattices with more types of traps and to a model where the trapping occurs during special steps finally the green s function at the origin g 0 z for a finite lattice with periodic boundary conditions which enters into the main expressions is studied more closely a generalization of an expression for g 0 1 for the square lattice given by montroll to values of z different from but close to 1 is derived

sequential systems of linear equations method for general constrained optimization without strict complementarity in this paper based on an l1 l hybrid exact penalty function we proposed an infeasible ssle method for general constrained optimization an automatic adjustment rule is incorporated in the algorithm for the choice of the penalty parameter which ensures that the penalty parameter be updated only finitely many times we also extend the facchinei fischer kanzow active set identification technique to general constrained optimization and a corresponding identification function is given at each iteration only two or three reduced linear equations with the same coefficients are solved to obtain the search direction under the linear independence condition the sequence generated by the new algorithm globally converges to a kkt point in particular the convergence rate is proved to be one step superlinear without assuming the strict complementarity and under a condition weaker than the strong second order sufficiency condition some preliminary numerical results indicate that the new algorithm is quite promising

first passage properties of mortal random walks ballistic behavior effective reduction of dimensionality and scaling functions for hierarchical graphs we consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites the configuration comprising the graph the starting point of the walk and the locations of the trap sites is taken to be exactly self similar as one goes from one generation of the family to the next under these circumstances the total probability that the walker hits a trap is determined exactly as a function of the single step survival probability q of the mortal walker on the nth generation graph of the family this probability is shown to be given by the nth iterate of a certain scaling function or map q f q the properties of the map then determine in each case the behavior of the trapping probability the mean time to trapping the temporal scaling factor governing the random walk dimension on the graph and other related properties the formalism is illustrated for the cases of a linear hierarchical lattice and the sierpinski graphs in two and three euclidean dimensions we find an effective reduction of the random walk dimensionality due to the ballistic behavior of the surviving particles induced by the mortality constraint the relevance of this finding for experiments involving travel times of particles in diffusion decay systems is discussed

a qp free globally convergent locally superlinearly convergent algorithm for inequality constrained optimization an algorithm is proposed for the minimization of a smooth function subject to smooth inequality constraints unlike sequential quadratic programming type methods this algorithm does not involve the solution of quadratic programs but merely that of linear systems of equations locally the iteration can be viewed as a perturbation of a quasi newton iteration on both the primal and dual variables for the solution of the equalities in the kuhn tucker first order conditions of optimality it is observed that provided the current iterate is feasible and the current multiplier estimates are strictly positive the primal component of the quasi newton direction is a direction of descent for the objective function this fact is used to induce global convergence without the need of a surrogate merit function a careful bending of the search direction prevents any maratos like effect and local superlinear convergence is proven while the algorithm requires that an initial feasible point be available the succe

a feasible active set qp free method for nonlinear programming we propose a monotone descent active set qp free method for inequality constrained optimization that ensures the feasibility of all iterates and allows for iterates on the boundary of the feasible set the study is motivated by the facchinei fischer kanzow active set identification technique for nonlinear programming and variational inequalities f facchinei a fischer and c kanzow siam j optim 9 1999 pp 14 32 distinguishing features of the proposed method compared with existing qp free methods include lower subproblem costs and a fast convergence rate under milder assumptions specifically four reduced linear systems with a common coefficient matrix involving only constraints in a working set are solved at each iteration to determine the working set the method makes use of multipliers from the last iteration eliminating the need to compute a new estimate and no additional linear systems are solved to select linearly independent constraint gradients a new technique is presented to avoid possible ill conditioned newton systems caused by dual degeneracy it is shown that the method converges globally to kkt points under the linear independence constraint qualification licq and the asymptotic rate of convergence is q superlinear under an additional strong second order sufficient condition ssosc without strict complementarity

localized partial traps in diffusion processes and random walks reaction diffusion equations in which the reaction is described by a sink term consisting of a sum of delta functions are studied it is shown that the laplace transform of the reactive green s function can be analytically expressed in terms of the green s function for diffusion in the absence of reaction moreover a simple relation between the green s functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained several applications are presented and the formalism is used to establish the relationship between the time dependent geminate recombination yield and the bimolecular reaction rate for diffusion influenced reactions finally an analogous development for lattice random walks is presented