errata in implicit multifunction theorems for the sensitivity analysis of variational conditions this note corrects a faulty application of the theory in 3 to the sensitivity analysis of stationary points associated with nonlinear programs corrected sufficient conditions are given for the local upper lipschitz continuity of these stationary points

convergence and stability of iterative algorithms of generalized set valued variational like inclusions in banach spaces abstract in this paper we give the notion of p proximal mapping an extension of p proximal mapping given by ding and xia j comput appl math 147 2002 369 for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space and prove its existence and lipschitz continuity further we consider a class of generalized set valued variational like inclusions in banach space and show its equivalence with a class of implicit wiener hopf equations using the concept of p proximal mapping using this equivalence we propose a new class of iterative algorithms for the class of generalized set valued variational like inclusions furthermore we prove the existence of solution of generalized set valued variational like inclusions and discuss the convergence criteria and the stability of the iterative algorithm

quantitative stability analysis of stochastic quasi variational inequality problems and applications we consider a parametric stochastic quasi variational inequality problem sqvip for short where the underlying normal cone is defined over the solution set of a parametric stochastic cone system we investigate the impact of variation of the probability measure and the parameter on the solution of the sqvip by reformulating the sqvip as a natural equation and treating the orthogonal projection over the solution set of the parametric stochastic cone system as an optimization problem we effectively convert stability of the sqvip into that of a one stage stochastic program with stochastic cone constraints under some moderate conditions we derive holder outer semicontinuity and continuity of the solution set against the variation of the probability measure and the parameter the stability results are applied to a mathematical program with stochastic semidefinite constraints and a mathematical program with sqvip constraints

multipole expansions for the fokker planck landau operator we give a sequence of operators approximating the fokker planck landau collision operator this sequence is obtained by aplying the fast multipole method based on the work by greengard and rokhlin 17 and tends to the exact fokker planck landau operator with an arbitrary accuracy these operators satisfy the physical properties such as the conservation of mass momentum energy and the decay of the entropy furthermore the quadratic structure due to the velocity coupling in the expression of the fokker planck landau operator is removed in the approximating operators this fact reduces seriously the computationnal cost of numerical simulations of the fokker planck landau equation finally we give numerical conservative and entropy discretizations solving the homogeneous fokker planck landau equation using the fast multipole method in addition to the deterministic character of these approximations they give satisfactory results in terms of accuracy and cpu time

numerical algorithms for axisymmetric fokker planck landau operators we establish a simplified form of the axisymmetric fokker planck landau operator in doing so we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three dimensional operator a symmetrized version of this formulation leads to a class of numerical schemes which satisfy these physical properties at the discrete level fast numerical algorithms used in previous works are shown to be efficient in the cylindrical geometry finally some numerical tests are presented at the end of this paper

explicit serre duality on complex spaces abstract in this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization as well as a new analytic proof of serre duality on any reduced pure n dimensional paracompact complex space x at the core of the paper is the introduction of certain fine sheaves b x n q of currents on x of bidegree n q such that the dolbeault complex b x n becomes in a certain sense a dualizing complex in particular if x is cohen macaulay then b x n is an explicit fine resolution of the grothendieck dualizing sheaf

homotopy method for solving variational inequalities with bounded box constraints abstract in this paper using the gabriel more smoothing function of the median function a smooth homotopy method for solving nonsmooth equation reformulation of bounded box constrained variational inequality problem vip l u f is given without any monotonicity condition on the defining map f for starting point chosen almost everywhere in r n existence and convergence of the homotopy pathway are proven nevertheless it is also proven that if the starting point is chosen to be an interior point of the box the proposed homotopy method can also serve as an interior point method

conservative finite difference schemes for the fokker planck equations not violating the law of an increasing entropy abstract two finite difference schemes for the fokker planck equation in the case of an isotropic function of the charge particles are constructed these schemes are first order accurate with respect to time and second order accurate with respect to a e 2 the schemes conserve the number of particles and energy and the entropy change is nonnegative a relation between the incresing entropy law and the stability of the finite difference schemes is established

mathematical foundations of nonsmooth embedding methods this paper establishes a mathematical foundation for application of the well known classical embedding approach to a class of nonsmooth functions using a recently developed analogue of the derivative in cases where the functions involved fail to be differentiable in the usual sense as part of this development we show how to obtain an extension to this case of the classical hadamard theorem giving conditions for a map of n to itself to be a homeomorphism

abelian differentials on singular varieties and variations on a theorem of lie griffiths we compare various notions of meromorphic and holomorphic differential forms on singular analytic varieties in particular we find that every meromorphic form gives rise to a canonical principal value current with support in the variety demanding that this current be closed we obtain a useful analytic description of the dualizing sheaf we then go on to generalize the lie griffiths theorem on one hand it is shown that a rational trace is enough to ensure algebraicity of the data on the other hand we prove that zero trace implies that the form is holomorphic in the sense of currents in fact we prove a more general local version of the theorem

variational conditions under the constant rank constraint qualification this paper studies solution properties of a parametric variational condition under the constant rank constraint qualification crcq and properties of its underlying set we start by showing that if the crcq holds at a point in a fixed set then there exists a one to one correspondence between the collection of nonempty faces of the normal cone to the set at that point and the collection of active index sets at points nearby we then study the behavior of the euclidean projector and prove under the crcq that the set of multipliers associated with the euclidean projection is locally a continuous multifunction following that we apply the degree theory to a localized normal map to show that the combination of the crcq and the so called strong coherent orientation condition suffices for the parametric variational condition to have a locally unique continuous solution which is selected from finitely many c1 functions applications of this result under additional assumptions extend or recover some earlier results on parametric variational inequalities

nonsingularity and symmetry for linear normal maps normal maps are single valued generally nonsmooth functions expressing conditions for the solution of variational problems such as those of optimization or equilibrium normal maps arising from linear transformations are particularly important both in their own right and as predictors of the behavior of related nonlinear normal maps they are called locally or globally nonsingular if the functions appearing in them are local or global homeomorphisms satisfying a lipschitz condition we show here that when the linear transformation giving rise to such a normal map has a certain symmetry property the necessary and sufficient condition for nonsingularity takes a particularly simple and convenient form being simply a positive definiteness condition on a certain subspace

first and second order analysis of nonlinear semidefinite programs in this paper we study nonlinear semidefinite programming problems convexity duality and first order optimality conditions for such problems are presented a second order analysis is also given second order necessary and sufficient optimality conditions are derived finally sensitivity analysis of such programs is discussed

the bar partial equation on a non reduced analytic space let x be a possibly non reduced analytic space of pure dimension we introduce a notion of overline partial equation on x and prove a dolbeault grothendieck lemma we obtain fine sheaves mathcal a x q of 0 q currents so that the associated dolbeault complex yields a resolution of the structure sheaf mathscr o x our construction is based on intrinsic semi global koppelman formulas on x

residue currents with prescribed annihilator ideals on singular varieties given an ideal mathcal j on a complex manifold andersson and wulcan constructed explicitly a current r mathcal j such that the annihilator of r mathcal j is mathcal j generalizing the duality theorem for coleff herrera products we describe a way to generalize this construction to ideals on singular varieties

solution dependence on initial conditions in differential variational inequalities in the first part of this paper we establish several sensitivity results of the solution x t to the ordinary differential equation ode initial value problem ivp dx dt f x x 0 as a function of the initial value for a nondifferentiable f x specifically we show that for xi t equiv x t xi 0 0 leq t leq t a if f is b differentiable on xi t then so is the solution operator x t at 0 b if f is semismooth on xi t then so is x t at 0 c if f has a linear newton approximation on xi t then so does x t at 0 moreover the linear newton approximation of the solution operator can be obtained from the solution of a linear differential inclusion in the second part of the paper we apply these ode sensitivity results to a differential variational inequality dvi and discuss a the existence uniqueness and lipschitz dependence of solutions to subclasses of the dvi subject to boundary conditions via an implicit function theorem for semismooth equations and b the convergence of a nonsmooth shooting method for numerically computing such boundary value solutions

splitting methods for pseudomonotone mixed variational inequalities we consider and analyze some new splitting methods for solving monotone mixed variational inequalities by using the technique of updating the solution the modified methods converge for monotone and pseudomonotone continuous operators the new splitting methods differ from the existing splitting methods the new results are versatile and proof of convergence is very simple

a smoothing homotopy method for solving variational inequalities abstract in this paper a new homotopy method for solving the variational inequality problem vip x f find y x such that y y t f y 0 for all y x where x is a nonempty closed convex subset of r n and f r n r n is a continuously differentiable mapping is proposed the homotopy equation is constructed based on the smooth approximation to robinson s normal equation of variational inequality problem where the smooth approximation function p x of the projection function x x is an arbitrary one such that for any 0 and x r n p x int x under a weak condition on the defining mapping f which is needed for the existence of a solution to vip x f for the starting point chosen almost everywhere in r n existence and convergence of a smooth homotopy pathway to a solution of vip x f are proved several numerical experiments indicate that the method is efficient

an efficient explicit numerical scheme for diffusion type equations with a highly inhomogeneous and highly anisotropic diffusion tensor abstract a locally split step explicit lsse algorithm was developed for efficiently solving a multi dimensional advection diffusion type equation involving a highly inhomogeneous and highly anisotropic diffusion tensor which makes the problem very ill conditioned for standard implicit methods involving the iterative solution of large linear systems the need for such an optimized algorithm arises in particular in the frame of thermonuclear fusion applications for the purpose of simulating fast charged particle slowing down with an ion fokker planck code the lsse algorithm is presented in this paper along with the results of a model slowing down problem to which it has been applied

a homotopy continuation method for solving normal equations in this paper we present a continuation method for solving normal equations generated byc 2 functions and polyhedral convex sets we embed the normal map into a homotopyh and study the existence and characteristics of curves inh 1 0 starting at a specificd point we prove the convergence of such curves to a solution of the normal equation under some conditions on the polyhedral convex setc and the functionf we prove that the curve will have finite are length if the normal map associated with the derivative df and the critical conek is coherently oriented at each zero of the normal mapf c inside a certain ball of n 1998 the mathematical programming society inc published by elsevier science b v

augmented lagrangian methods under the constant positive linear dependence constraint qualification two augmented lagrangian algorithms for solving kkt systems are introduced the algorithms differ in the way in which penalty parameters are updated possibly infeasible accumulation points are characterized it is proved that feasible limit points that satisfy the constant positive linear dependence constraint qualification are kkt solutions boundedness of the penalty parameters is proved under suitable assumptions numerical experiments are presented

linear stability of generalized equations part i basic theory dedicated to anthony v fiacco on the occasion of his 65th birthday we consider a class of generalized equations involving set valued maps which formulate many problems from mathematical programming complementarity theory and mathematical economics many results concerning the stability behavior of the solution sets of this class of generalized equations have been established mainly focusing on qualitative characterizations we develop a theory concentrating on quantitative characterizations of the stability behavior of solutions of generalized equations and establish conditions which ensure the solution set of a generalized equation is quantitatively stable in part ii of the paper we use the concepts and methods developed here to treat norlinear programming problems

maximum rank of a legendrian web abstract we propose the legendrian web in a contact three manifold as a second order generalization of the planar web an abelian relation for a legendrian web is analogously defined as an additive equation among the first integrals of its foliations for a class of legendrian d webs defined by simple second order ode s we give an algebraic construction of d d 1 d 2 2 d 3 6 linearly independent abelian relations we then employ the method of local differential analysis and the theory of linear differential systems to show that d is the maximum rank of a legendrian d web in the complex analytic category we give a possible projective geometric interpretation of d as an analogue of castelnuovo bound for degree 2 d surfaces in the 3 quadric q 3 p 4 via the duality between p 3 and q 3 associated with the rank two complex simple lie group sp 2 c the legendrian 3 webs of maximum rank three are analytically characterized and their explicit local normal forms are found for an application we give an alternative characterization of a darboux super integrable metric as a two dimensional riemannian metric g which admits a mate metric g such that a legendrian 3 web naturally associated with the geodesic foliations of the pair g has maximum rank

weighted koppelman formulas and the equation on an analytic space let x be an analytic space of pure dimension we introduce a formalism to generate intrinsic weighted koppelman formulas on x that provide solutions to the partial derivative over bar equation we obtain new existence results for the partial derivative over bar equation as well as new proofs of various known results c 2011 elsevier inc all rights reserved

iterative algorithms for a new class of extended general nonconvex set valued variational inequalities abstract some new classes of extended general nonconvex set valued variational inequalities and the extended general wiener hopf inclusions are introduced by the projection technique equivalence between the extended general nonconvex set valued variational inequalities and the fixed point problems as well as the extended general nonconvex wiener hopf inclusions is proved then by using this equivalent formulation we discuss the existence of solutions of the extended general nonconvex set valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set valued variational inequalities we also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set valued variational inequalities the results presented in this paper extend and improve some known results from the literature

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

solving variational inequality problems via smoothing nonsmooth reformulations it has long been known that variational inequality problems can be reformulated as nonsmooth equations recently locally high order convergent newton methods for nonsmooth equations have been well established via the concept of semismoothness when the constraint set of the variational inequality problem is a rectangle several locally convergent newton methods for the reformulated nonsmooth equations can also be globalized in this paper our main aim is to provide globally and locally high order convergent newton methods for solving variational inequality problems with general constraints to achieve this we first prove via convolution that these nonsmooth equations can be well approximated by smooth equations which have desirable properties for the design of newton methods we then reformulate the variational inequality problems as equivalent smoothing nonsmooth equations and apply newton type methods to solve the latter systems and so the variational inequality problems stronger convergence results have been obtained

an entropy scheme for the fokker planck collision operator of plasma kinetic theory we propose a finite difference scheme to approximate the fokker planck collision operator in 3 velocity dimensions the principal feature of this scheme is to provide a decay of the numerical entropy as a consequence it preserves the collisional invariants and its stationary solutions are the discrete maxwellians we consider both the whole velocity space problem and the bounded velocity problem in the latter case we provide artificial boundary conditions which preserve the decay of the entropy

convergence of a difference scheme for the vlasov poisson fokker planck system in one dimension a finite difference scheme is proposed for the periodic one dimensional vlasov poisson fokker planck system which is related to the scheme in c cheng and g knorr em j comp phys 22 1976 pp 330 351 the density f left t x v right and the electric field e left t x right are shown to converge to the exact solution values in l 2 and l infty respectively the rate of convergence is essentially first order this scheme has been implemented in j schaeffer center for nonlinear analysis research report 97 na 004 carnegie mellon university 1997 and compares favorably with a random particle method

piecewise affine bijections of rn and the equation sx tx y we prove two criteria for bijectivity of piecewise affine maps f of rn it is assumed that det f has the same nonzero sign everywhere the first criterion is based solely on the branching properties of the partition of rn into domains of linearity of f the second one concerns the map itself and depends on the images under f of certain two dimensional angles this generalizes and improves results of r schramm the methods are topological our results imply k g murty s solution of the linear complementarity problem and some other partly known facts which we show are equivalent to it for example the map x sx tx is bijective iff all principal minors of s 1t are strictly positive

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

on the asymptotics of constrained local m estimators we discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and more generally m estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set s we give a counterexample showing that regularity of s in the sense of clarke is not sufficient for asymptotic equivalence of n consistent locally optimal m estimators we argue further that stronger properties such as so called near convexity or prox regularity of s are required in order to ensure that any two n consistent locally optimal m estimators have the same asymptotics

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

global effective versions of the briancon skoda huneke theorem we prove global effective versions of the briancon skoda huneke theorem our results extend to singular varieties a result of hickel on the membership problem in polynomial ideals in cn and a related theorem of ein and lazarsfeld for smooth projective varieties the proofs rely on known geometric estimates and new results on multivariable residue calculus

sensitivity analysis of parameterized variational inequalities in this paper we discuss local uniqueness continuity and differentiability properties of solutions of parameterized variational inequalities generalized equations to this end we use two types of techniques one approach consists in formulating variational inequalities in a form of optimization problem based on regularized gap functions and applying a general theory of perturbation analysis of parameterized optimization problems another approach is based on a theory of contingent outer graphical derivatives and some results about differentiability properties of metric projections

tissus algebriques exceptionnels in pirio and trepreau int math res not imrn doi 10 1093 imrn rnu066 2014 it has been proved that for r 1 n ge 2 and d ge r 1 n 1 2 a d web of t ype r n with maximal rank is algebraizable in the classical sense except maybe when n ge 3 and d r 2 n 1 1 in the present paper one considers this particular case under these hypotheses on n and d one constructs some examples of exceptional algebraic webs these are generalized algebraic webs of maximal rank that are not algebraizable in the classical sense

three step iterative algorithms for multivalued quasi variational inclusions in this paper we suggest and analyze some new classes of three step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique new iterative algorithms include the ishikawa mann and noor iterations for solving variational inclusions inequalities and optimization problems as special cases the results obtained in this paper represent an improvement and a significant refinement of previously known results

on the intersection of algebraic curves and hypersurfaces many classical theorems about the intersection of plane algebraic curves can be derived from and generalized by the algebraic theory of residues in higher dimensional spaces one obtains results about the intersection of curves and hypersurfaces in various degrees of generality this was pointed out f i in s gh k2 and hu in the present note we wish to prove higher dimensional analogues of theorems of waring g humbert and reiss for arbitrary curves in affine n space and their intersection with hypersurfaces see theorems 4 1 5 1 and 6 2 below by a curve hypersurface we mean a closed subscheme in projective or affine n space of pure dimension 1 pure codimension 1 having no embedded components our considerations are based on the residue theorem for complete integral algebraic curves

degree theory for generalized variational inequalities and applications in this paper a degree theory for finite dimensional generalized variational inequalities is built and employed to prove some results on solution existence and solution stability

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

on existence and uniqueness of stationary points in semi infinite optimization the paper deals with semi infinite optimization problems which are defined by finitely many equality constraints and infinitely many inequality constraints we generalize the concept of strongly stable stationary points which was introduced by kojima for finite problems it refers to the local existence and uniqueness of a stationary point for each sufficiently small perturbed problem where perturbations up to second order are allowed under the extended mangasarian fromovitz constraint qualification we present equivalent conditions for the strong stability of a considered stationary point in terms of first and second derivatives of the involved functions in particular we discuss the case where the reduction approach is not satisfied

existence and differentiability of metric projections in hilbert spaces this paper considers metric projections onto a closed subset s of a hilbert space if the set s is convex then it is well known that the corresponding metric projections always exist unique and directionally differentiable at boundary points of s these properties of metric projections are considered for possibly nonconvex sets s in particular existence and directional differentiability of metric projections for certain classes of sets are established and will be referred to as nearly convex sets

iterative solving of generalized equations with calm solution mappings abstract we present an iterative procedure for solving in finite dimensions generalized equations of the form 0 f x f x where f is a continuous function while f stands for a closed set valued mapping assuming that f belongs to a class of functions admitting a certain type of approximation and that the solution set of satisfies a calmness type property we show that the method we consider is superlinearly convergent to a solution of

new extragradient type methods for general variational inequalities in this paper we consider and analyze a new class of extragradient type methods for solving general variational inequalities the modified methods converge for pseudomonotone operators which is weaker condition than monotonicity our proof of convergence is very simple as compared with other methods the proposed methods include several new and known methods as special cases our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems

a class of projection methods for general variational inequalities abstract in this paper we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the wiener hopf equations technique the modified methods converge for pseudomonotone operators our proof of convergence is very simple as compared with other methods the proposed methods include several known methods as special cases

homotopy method for solving ball constrained variational inequalities abstract in this paper we present a smoothing homotopy method for solving ball constrained variational inequalities by utilizing a similar chen harker kanzow smale function to smooth robinson s normal equation without any monotonicity condition on the defining map f for the starting point chosen almost everywhere in r n the existence and convergence of the homotopy pathway are proven numerical experiments illustrate that the method is feasible and effective

on the lipschitzian properties of polyhedral multifunctions in this paper we show that for a polyhedral multifunctionf rn rm with convex range the inverse functionf 1 is locally lower lipschitzian at every point of the range off equivalently lipschitzian on the range off if and only if the functionf is open as a consequence we show that for a piecewise affine functionf rn rn f is surjective andf 1 is lipschitzian if and only iff is coherently oriented an application via robinson s normal map formulation leads to the following result in the context of affine variational inequalities the solution mapping as a function of the data vector is nonempty valued and lipschitzian on the entire space if and only if the solution mapping is single valued this extends a recent result of murthy parthasarathy and sabatini proved in the setting of linear complementarity problems

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

a dolbeault grothendieck lemma on complex spaces via koppelman formulas let x be a complex space of pure dimension we introduce fine sheaves a x q of 0 q currents which coincides with the sheaves of smooth forms on the regular part of x so that the associated dolbeault complex yields a resolution of the structure sheaf hol x our construction is based on intrinsic and quite explicit semi global koppelman formulas

on bilevel programming part i general nonlinear cases this paper is concerned with general nonlinear nonconvex bilevel programming problems blpp we derive necessary and sufficient conditions at a local solution and investigate the stability and sensitivity analysis at a local solution in the blpp we then explore an approach in which a bundle method is used in the upper level problem with subgradient information from the lower level problem two algorithms are proposed to solve the general nonlinear blpp and are shown to converge to regular points of the blpp under appropriate conditions the theoretical analysis conducted in this paper seems to indicate that a sensitivity based approach is rather promising for solving general nonlinear blpp