a new neural network for solving linear and quadratic programming problems a new neural network for solving linear and quadratic programming problems is presented and is shown to be globally convergent the new neural network improves existing neural networks for solving these problems it avoids the parameter turning problem it is capable of achieving the exact solutions and it uses only simple hardware in which no analog multipliers for variables are required furthermore the network solves both the primal problems and their dual problems simultaneously

strong duality and kkt conditions in nonconvex optimization with a single equality constraint and geometric constraint some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established in particular a hidden convexity of the conic hull of joint range of the pair of functions associated to the original problem is obtained applications to derive a characterization of the validity of kkt conditions without standard constraints qualification are also discussed it goes beyond the exact penalization technique several examples showing our results provide much more information than those appearing elsewhere are given finally the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail

ladder operators normal ordering problem for quantum deformed systems and the q p generalization of the stirling and bell numbers we resolve the ladder operators normal ordering problem for strings in the form for q p deformed supersymmetric and shape invariant potential systems where n is a positive integer we provide exact and explicit expressions for their normal form where in all are at the right hand side and find that the solution involves expansion coefficients sequence which corresponds to the generalization for any q p deformed shape invariant potential system of the classical stirling and bell numbers we show that these numbers are given for expressions depending on parameters related to the forms of supersymmetric partner potentials and the system quantum deformation we apply the general formalism to poschl teller morse and scarf potential systems

a novel neural network for nonlinear convex programming in this paper we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method the main idea is to convert the convex programming problem into a variational inequality problem then a dynamical system and a convex energy function are constructed for resulting variational inequality problem it is shown that the proposed neural network is stable in the sense of lyapunov and can converge to an exact optimal solution of the original problem compared with the existing neural networks for solving the nonlinear convex programming problem the proposed neural network has no lipschitz condition no adjustable parameter and its structure is simple the validity and transient behavior of the proposed neural network are demonstrated by some simulation results

group averaging in the p q oscillator representation of sl 2 r we investigate refined algebraic quantization with group averaging in a finite dimensional constrained hamiltonian system that provides a simplified model of general relativity the classical theory has gauge group sl 2 r and a distinguished o p q observable algebra the gauge group of the quantum theory is the double cover of sl 2 r and its representation on the auxiliary hilbert space is isomorphic to the p q oscillator representation when p 2 q 2 and p q 0 mod 2 we obtain a physical hilbert space with a nontrivial representation of the o p q quantum observable algebra for p q 1 the system provides the first example known to us where group averaging converges to an indefinite sesquilinear form

refined algebraic quantization in the oscillator representation of sl 2 r we investigate refined algebraic quantization raq with group averaging in a constrained hamiltonian system with unreduced phase space t r4 and gauge group sl 2 r the reduced phase space m is connected and contains four mutually disconnected regular sectors with topology r s1 but these sectors are connected to each other through an exceptional set where m is not a manifold and where m has non hausdorff topology the raq physical hilbert space hphys decomposes as hphys hi where the four subspaces hi naturally correspond to the four regular sectors of m the raq observable algebra aobs represented on hphys contains natural subalgebras represented on each hi the group averaging takes place in the oscillator representation of sl 2 r on l2 r2 2 and ensuring convergence requires a subtle choice for the test state space the classical analog of this choice is to excise from m the exceptional set while nevertheless retaining information about the connections between the regular sectors a quantum

the brs method and geometric quantization some examples we recall the method of quantization of constraints as outlined by kostant and sternberg we discuss various examples to test compatibility between geometric quantization and this procedure in almost all cases reduction and quantization commute

constraint rescaling in refined algebraic quantisation momentum constraint we investigate refined algebraic quantisation within a family of classically equivalent constrained hamiltonian systems that are related to each other by rescaling a momentum type constraint the quantum constraint is implemented by a rigging map that is motivated by group averaging but has a resolution finer than what can be peeled off from the formally divergent contributions to the averaging integral three cases emerge depending on the asymptotics of the rescaling function i quantisation is equivalent to that with identity scaling ii quantisation fails owing to nonexistence of self adjoint extensions of the constraint operator iii a quantisation ambiguity arises from the self adjoint extension of the constraint operator and the resolution of this purely quantum mechanical ambiguity determines the superselection structure of the physical hilbert space prospects of generalising the analysis to systems with several constraints are discussed

lagrange multipliers and calmness conditions of order p in this paper by assuming that a non lipschitz penalty function is exact new conditions for the existence of lagrange multipliers are established for an inequality and equality constrained continuously differentiable optimization problem this is done by virtue of a first order necessary optimality condition of the penalty problem which is obtained by estimating dini upper directional derivatives of the penalty function in terms of taylor expansions and a farkas lemma relations among the obtained results and some well known constraint qualifications are discussed

the zero duality gap property and lower semicontinuity of the perturbation function we examine the validity of the zero duality gap properties for two important dual schemes a generalized augmented lagrangian dual scheme and a nonlinear lagrange type dual scheme the necessary and sufficient conditions for the zero duality gap property to hold are established in terms of the lower semicontinuity of the perturbation functions

solving quadratic programming problems by delayed projection neural network in this letter the delayed projection neural network for solving convex quadratic programming problems is proposed the neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem three examples show the effectiveness of the proposed network

a unified augmented lagrangian approach to duality and exact penalization in this paper the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real valued function are established via a generalized augmented lagrangian and corresponding generalized augmented lagrangian problems in which no convexity is imposed on the augmenting function these results further imply a zero duality gap property between the primal problem and the generalized augmented lagrangian dual problem a necessary and sufficient condition for the exact penalty representation in the framework of a generalized augmented lagrangian is obtained in the context of constrained programs we show that generalized augmented lagrangians present a unified approach to several classes of exact penalization results some equivalences among exact penalization results are obtained

characterizing fj and kkt conditions in nonconvex mathematical programming with applications in this paper we analyze the fritz john and karush kuhn tucker kkt conditions for a g teaux differentiable nonconvex optimization problem with inequality constraints and a geometric constraint set the fritz john condition is characterized in terms of an alternative theorem which covers beyond standard situations while characterizations of kkt conditions without assuming constraints qualifications are related to strong duality of a suitable linear approximation of the given problem and the properties of its associated image mapping such characterizations are suitable for dealing with some problems in structural optimization where most of the known constraint qualifications fail in particular several examples are given showing the usefulness and optimality in a certain sense of our results which provide much more information than those including the mordukhovich normal cone or clarke s appearing elsewhere the case with a single inequality constraint is discussed in detail by establishing

quantization of diffeomorphism invariant theories of connections with local degrees of freedom quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphism constraint is solved the space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions this provides in particular a quantization of the husain kucha model the main results also pave the way to quantization of other diffeomorphism invariant theories such as general relativity in the riemannian case i e signature the approach appears to contain all the necessary ingredients already in the lorentzian case it will have to be combined in an appropriate fashion with a coherent state transform to incorporate complex connections

an improved dual neural network for solving a class of quadratic programming problems and its k winners take all application this paper presents a novel recurrent neural network for solving a class of convex quadratic programming qp problems in which the quadratic term in the objective function is the square of the euclidean norm of the variable this special structure leads to a set of simple optimality conditions for the problem based on which the neural network model is formulated compared with existing neural networks for general convex qp the new model is simpler in structure and easier to implement the new model can be regarded as an improved version of the dual neural network in the literature based on the new model a simple neural network capable of solving the k winners take all k wta problem is formulated the stability and global convergence of the proposed neural network is proved rigorously and substantiated by simulation results

reduction quantization and nonunimodular groups it is shown that even in relatively nice cases the naive approach to the quantization of constraints is not correct in general i e the procedure that if f 0 is a classical constraint and f is the associated quantum operator then the quantum constraint is f 0 an explicit procedure for the quantization of constraints in the case of a configuration space with a symmetry group is provided and proven where the reduced configuration space is the orbit space it is not thought that the group acts freely merely that all isotropy subgroups are conjugated to each other

a one layer recurrent neural network with a discontinuous hard limiting activation function for quadratic programming in this paper a one layer recurrent neural network with a discontinuous hard limiting activation function is proposed for quadratic programming this neural network is capable of solving a large class of quadratic programming problems the state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints in addition a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming simulation results on numerical examples and support vector machine svm learning show the effectiveness and performance of the neural network

solving generally constrained generalized linear variational inequalities using the general projection neural networks generalized linear variational inequality glvi is an extension of the canonical linear variational inequality in recent years a recurrent neural network nn called general projection neural network gpnn was developed for solving glvis with simple bound often box type or sphere type constraints the aim of this paper is twofold first some further stability results of the gpnn are presented second the gpnn is extended for solving glvis with general linear equality and inequality constraints a new design methodology for the gpnn is then proposed furthermore in view of different types of constraints approaches for reducing the number of neurons of the gpnn are discussed which results in two specific gpnns moreover some distinct properties of the resulting gpnns are also explored based on their particular structures numerical simulation results are provided to validate the results

a generalized second order derivative in nonsmooth optimization in this work a new notion of generalized second order directional derivative and generalized hessian for nonsmooth real valued functions is studied the general properties of these mathematical objects are investigated together with some calculus rules that may facilitate their practical computation two applications of these derivatives in optimization theory are considered first to obtaining necessary and sufficient second order optimality conditions for problems with or without constraints and second to extending the newton method for the minimization of a mathcal c 1 1 function

global exponential stability of neural networks with globally lipschitz continuous activations and its application to linear variational inequality problem this paper investigates the existence uniqueness and global exponential stability ges of the equilibrium point for a large class of neural networks with globally lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations the provided sufficient condition for ges is mild and some conditions easily examined in practice are also presented the ges of neural networks in the case of locally lipschitz continuous activations is also obtained under an appropriate condition the analysis results given in the paper extend substantially the existing relevant stability results in the literature and therefore expand significantly the application range of neural networks in solving optimization problems as a demonstration we apply the obtained analysis results to the design of a recurrent neural network rnn for solving the linear variational inequality problem vip defined on any nonempty and closed box set which includes the box constrained quadratic programming and the linear complementarity problem as the special cases it can be inferred that the linear vip has a unique solution for the class of lyapunov diagonally stable matrices and that the synthesized rnn is globally exponentially convergent to the unique solution some illustrative simulation examples are also given

an algebraic extension of dirac quantization examples an extension of the dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in dirac s original proposal these issues play an important role especially in the context of nonlinear diffeomorphism invariant theories such as general relativity recently an extension of the required type was proposed using algebraic quantization methods in this paper the key conceptual and technical aspects of the algebraic program are illustrated through a number of finite dimensional examples the choice of examples and some of the analysis is motivated by certain peculiar problems endemic to quantum gravity however prior knowledge of general relativity is not assumed in the main discussion indeed the methods introduced and conclusions arrived at are applicable to any system with first class constraints in particular they resolve certain technical issues which are present also in the reduced phase space approach to quantization of these systems

existence of augmented lagrange multipliers reduction to exact penalty functions and localization principle in this article we present new general results on existence of augmented lagrange multipliers we define a penalty function associated with an augmented lagrangian and prove that under a certain growth assumption on the augmenting function an augmented lagrange multiplier exists if and only if this penalty function is exact we also develop a new general approach to the study of augmented lagrange multipliers called the localization principle the localization principle allows one to study the local behaviour of the augmented lagrangian near global optimal solutions of the initial optimization problem in order to prove the existence of augmented lagrange multipliers

refined algebraic quantisation in a system with nonconstant gauge invariant structure functions in a previous work j louko and e martinez pascual constraint rescaling in refined algebraic quantisation momentum constraint j math phys 52 123504 2011 10 1063 1 3664336 refined algebraic quantisation raq within a family of classically equivalent constrained hamiltonian systems that are related to each other by rescaling one momentum type constraint was investigated in the present work the first steps to generalise this analysis to cases where more constraints occur are developed the system under consideration contains two momentum type constraints originally abelian where rescalings of these constraints by a non vanishing function of the coordinates are allowed these rescalings induce structure functions at the level of the gauge algebra providing a specific parametrised family of real valued scaling functions the implementation of the corresponding rescaled quantum momentum type constraints is performed using raq when the gauge algebra i remains abelian and ii undergoes int

recurrent neural network for non smooth convex optimization problems with application to the identification of genetic regulatory networks a recurrent neural network is proposed for solving the non smooth convex optimization problem with the convex inequality and linear equality constraints since the objective function and inequality constraints may not be smooth the clarke s generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network it is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the lagrangian saddle point theorem under weak conditions the proposed neural network is proved to be stable and the state of the neural network is convergent to one of its equilibrium points compared with the existing neural network models for non smooth optimization problems the proposed neural network can deal with a larger class of constraints and is not based on the penalty method finally the proposed neural network is used to solve the identification problem of genetic regulatory networks which can be transformed into a non smooth convex optimization problem the simulation results show the satisfactory identification accuracy which demonstrates the effectiveness and efficiency of the proposed approach

group theoretical quantization and the example of a phase space s1 r the group theoretical quantization scheme is reconsidered by means of elementary systems already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group actions a systematic strategy for finding admissible group actions for particular subbundles of cotangent spaces is developed two dimensional prototypes of which are t r and s s1 r interpreted as restrictions of t r and t s1 to positive coordinate and momentum respectively in this framework and under an additional natural condition an so 1 2 action on s results as the unique admissible group action furthermore for symplectic manifolds which are specific parts of phase spaces with known quantum theory a simple projection method of quantization is formulated for t r and s equivalent results to those of more established but more involved quantization schemes are obtained the approach may be of interest e g in attempts to quantize g

optimality conditions via exact penalty functions in this paper we study kkt optimality conditions for constrained nonlinear programming problems and strong and mordukhovich stationarities for mathematical programs with complementarity constraints using l p penalty functions with 0 leq p leq1 we introduce some optimality indication sets by using contingent derivatives of penalty function terms some characterizations of optimality indication sets are obtained by virtue of the original problem data we show that the kkt optimality condition holds at a feasible point if this point is a local minimizer of some l p penalty function with p belonging to the optimality indication set our result on constrained nonlinear programming includes some existing results from the literature as special cases