a norm relaxed method of feasible directions for finely discretized problems from semi infinite programming abstract in this paper a class of finely discretized semi infinite programming sip problems is discussed combining the idea of the norm relaxed method of feasible directions mfd and the technique of updating discretization index set we present a new algorithm for solving the discretized semi infinite dsi problems from sip at each iteration the iteration point is feasible for the discretized problem and an improved search direction is computed by solving only one direction finding subproblem i e a quadratic program and some appropriate constraints are chosen to reduce the computational cost a high order correction direction can be obtained by solving another quadratic programming subproblem with only equality constraints under weak conditions such as mangasarian fromovitz constraint qualification mfcq the proposed algorithm possesses weak global convergence moreover the superlinear convergence is obtained under linearly independent constraint qualification licq and other assumptions in the end some elementary numerical experiments are reported

an efficient sequential quadratic programming algorithm for nonlinear programming in this paper a new feasible sequential quadratic programming fsqp algorithm is proposed to solve the nonlinear programming where a feasible descent direction is obtained by solving only one qp subproblem in order to avoid maratos effect a high order revised direction is computed by solving a linear system with involving some active constraints the theoretical analysis shows that global and superlinear convergence can be deduced

a new norm relaxed method of strongly sub feasible direction for inequality constrained optimization combining the norm relaxed method of feasible direction mfd with the idea of strongly sub feasible direction method we present a new convergent algorithm with arbitrary initial point for inequality constrained optimization at each iteration the new algorithm solves one direction finding subproblem dfs which always possesses a solution some good properties of the new algorithm are that it can unify automatically the operations of initialization phase i and optimization phase ii and the number of the functions satisfying the inequality constrains is nondecreasing particularly a feasible direction of descent can be obtained by solving dfs whenever the iteration point gets into the feasible set under some mild assumptions without the linear independence the global and strong convergence of the algorithm can be obtained

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

boundary controllability of sobolev type abstract nonlinear integrodifferential systems sufficient conditions are established for boundary controllability of various classes of sobolev type nonlinear systems including integrodifferential systems in banach spaces the results are obtained using the strongly continuous semigroup of operators and the banach contraction principle examples are provided to illustrate the theory

an efficient feasible directions algorithm for design synthesis a nonlinear optimization algorithm is described that combines the best features of the method of feasible directions and the generalized reduced gradient method the algorithm uses the direction finding subproblem from the method of feasible directions to find a search direction that is equivalent to that of the generalized reduced gradient method but without the need to add a large number of slack variables associated with inequality constraints this leads to a core efficient algorithm for the solution of optimization problems with a large number of inequality constraints also during the one dimensional search it is not necessary to separate the design space into dependent and independent variables using the present method the concept of infrequent gradient calculations is introduced as a means of gaining further optimization efficiency finally it is shown that using the basic direction finding algorithm contained in this method the sensitivity of the optimum design with respect to problem parameters can be obtained without the need for second derivatives or lagrange multipliers the optimization algorithm and sensitivity analysis is demonstrated by numerical example

a continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints in this paper it is shown that given a nonlinear programming problem with inequality constraints it is possible to construct a continuously differentiable exact penalty function whose global or local unconstrained minimizers correspond to global or local solutions of the constrained problem

a feasible descent sqp algorithm for general constrained optimization without strict complementarity in this paper a class of optimization problems with equality and inequality constraints is discussed firstly the original problem is transformed to an associated simpler problem with only inequality constraints and a parameter the later problem is shown to be equivalent to the original problem if the parameter is large enough but finite then a feasible descent sqp algorithm for the simplified problem is presented at each iteration of the proposed algorithm a master direction is obtained by solving a quadratic program which always has a feasible solution with two corrections on the master direction by two simple explicit formulas the algorithm generates a feasible descent direction for the simplified problem and a height order correction direction which can avoid the maratos effect without the strict complementarity then performs a curve search to obtain the next iteration point thanks to the new height order correction technique under mild conditions without the strict complementarity the globally and superlinearly convergent properties are obtained finally an efficient implementation of the numerical experiments is reported

a strategy for global convergence in a sequential quadratic programming algorithm n a previous work p boggs and j tolle siam j numer anal 21 1984 pp 1146 1161 the authors introduced a merit function for use with the sequential quadratic programming sqp algorithm for solving nonlinear programming problems here further theoretical justification including a global convergence theorem is provided in addition modifications are suggested that allow the efficient implementation of the merit function while maintaining the important convergence properties numerical results are presented demonstrating the effectiveness of the procedure

the theoretical analysis and algorithm on a class of optimal curve fitting problems in this paper the theory and algorithm on a class of optimal curve fitting problems which can be extensively applied to the engineering are established and completed with regard to the curve fitting problems the available theories and methods are largely concerned with the spline interpolation and linear or nonlinear least squares methods and there are lots of ripe results to my best knowledge however in view of the complexity the third method that is to resort to solve functional extremal problems remains completed both in theories and algorithms regarding the class of this problems that is here called as the optimal curve fitting problems under relaxation constraints the analytic expression of solution and solving algorithms were discussed in p cheng k c zhang on a class of constrained functional minimization problems and their numerical solution journal of optimization theory and applications 78 2 1993 p267 p287 p cheng kc zhang unified method for a kind of constrained functional minimization computing technology and automation 10 2 1991 13 25 k c zhang a numerical method for solving a class of variation problems with constraint and its application to engineering numerical mathematics a journal of chinese universities 11 2 1989 1 9 k c zhang the algorithm and analysis of numerical computation beijing science press 2003 pp 172 184 but the existence of optimal solution has not been solved so far in the paper with help of variational principle and convexity analysis we give the proof of existence in details and a different proof about the analytic expression of optimal solution moreover we prove that for every smoothing parameter m this class of optimal curve fitting problems is equivalent to solve a quadratic programming with a spherical constraint which usually appears in the trust region and sqp subproblems and its algorithms have been quite ripe therefore a novel algorithm different from zhang 2003 for this class problems is established finally we give an example of m 2 to validate our theory and method numerical test shows that the method is effective and practical

a decomposition algorithm for solving large scale quadratic programming problems in this paper an algorithm for solving large scale programming is proposed we decompose a large scale quadratic programming into a serial of small scale ones and then approximate the solution of the large scale quadratic programming via the solutions of these small scale ones it is proved that the accumulation point of the iterates generated by the algorithm is a global minimum point of the quadratic programming the algorithm has performed very well in numerical testing it is a new way of solving large scale quadratic programming problems

two new weak constraint qualifications and applications we present two new constraint qualifications cqs that are weaker than the recently introduced relaxed constant positive linear dependence rcpld cq rcpld is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally a major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a cq this is done in the first new cq which we call the constant rank of the subspace component crsc cq this new cq also preserves many of the good properties of rcpld such as local stability and the validity of an error bound we also introduce an even weaker cq called the constant positive generator cpg which can replace rcpld in the analysis of the global convergence of algorithms we close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods sequential quadratic programming augmented lagrangians

boundary controllability of differential equations with nonlocal condition for a semilinear boundary control system with a nonlocal condition using a banach fixed point theorem we prove the boundary controllable and we give an application

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

a new feasible descent algorithm combining sqp with generalized projection for optimization problems without strict complementarity in this paper optimization problems with nonlinear inequality constraints are discussed by combining the sequential quadratic programming sqp with an new generalized projection technique a new feasible descent algorithm for solving the problems is presented at each iteration of the new algorithm a convex quadratic program qp is solved and a master direction is obtained and an improved feasible descent direction is yielded by updating the master direction with an explicit formula and in order to avoid the maratos effect a height order correction direction is computed by another explicit formula of the master direction and the improved direction both this two correction formulas contain a new generalized projection technique under weaker conditions without the strict complementarity the new algorithm is proved to possess global convergence and superlinear convergence furthermore the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted

a recursive quadratic programming algorithm that uses differentiable exact penalty functions in this paper a recursive quadratic programming algorithm for solving equality constrained optimization problems is proposed and studied the line search functions used are approximations to fletcher s differentiable exact penalty function global convergence and local superlinear convergence results are proved and some numerical results are given

a strongly convergent norm relaxed method of strongly sub feasible direction for optimization with nonlinear equality and inequality constraints in this paper a class of optimization problems with nonlinear equality and inequality constraints is discussed firstly the original problem is transformed to an associated simpler auxiliary optimization problem with only inequality constraints and a penalty parameter and the later problem is showed to be equivalent to the original problem if the parameter is large enough but finite then combining the norm relaxed method of feasible direction mfd with the idea of method of strongly sub feasible direction mssfd we present an algorithm with arbitrary initial point for the original problem at each iteration of the auxiliary problem an improved search direction is obtained by solving one direction finding subproblem dfs i e a quadratic program which always possesses a solution in the process of iteration the feasibility of the iteration points is monotone increasing furthermore whenever an iteration point enters the feasible set the proposed algorithm reduces to a feasible and decent method for the auxiliary problem under some suitable assumptions the global and strong convergence of the proposed algorithm can be obtained finally some elementary numerical experiments are reported

incremental computation of squares and sums of squares an incremental algorithm for computation of sums of squares is presented that is suitable for both most significant bit msb first and least significant bit lsb first bit sequential operation by exploiting symmetry properties of numerical values and evaluation times in the bit product matrix it is shown how incremental multipliers can be converted to perform squaring at reduced hardware cost and sum of squaring at a hardware cost to that of scalar multiplication by the elimination of redundant computation existing hardware modules are either reduced in size or assigned to the evaluation of a second squaring computation the corresponding hardware architectures are derived from a simple conversion of existing incremental scalar multipliers this conversion process is less practical on standard serial parallel or serial pipeline multipliers a digit on line algorithm is outlined for magnitude extraction operations on plane vectors

a simple feasible sqp algorithm for inequality constrained optimization in this paper an sqp method generating feasible iterates is presented to solve the nonlinear inequality constrained optimization problems a new modified method which ensures the global and superlinear convergence is proposed by solving systems of linear equation instead of qp subproblems and linear squares problems here the search direction is a suitable combination of a descent direction a feasible direction and a second order revised direction the theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions

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

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

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

a superlinearly convergent method of feasible directions method of feasible directions mfd is one of the most important methods for solving engineering optimization problems there exist two types of mfd one has at most a linear convergence rate and the other has a superlinear convergence rate the former type includes zoutendijk s mfd topkis veinott s mfd pironneau polak s mfd cawood kostreva s norm relaxed mfd and a modified mfd the latter includes panier tits fsqp approaches however the price of the superlinearly convergent mfd for achieving superlinearity is rather high computational cost per single iteration this paper presents an algorithm based on the modified mfd the theoretical analysis shows that this algorithm is locally superlinearly convergent this algorithm has attained the same convergence rate as fsqp while it only needs to solve two subproblems instead of three subproblems in fsqp hence this algorithm should be computationally more efficient than fsqp

a superlinearly convergent norm relaxed method of quasi strongly sub feasible direction for inequality constrained minimax problems in this paper nonlinear minimax problems with inequality constraints are discussed combined the norm relaxed sqp method with the idea of strongly sub feasible directions method a new method of quasi strongly sub feasible directions mqssfd with arbitrary initial point for the discussed problems is presented at each iteration of the proposed algorithm an improved search direction is obtained by solving a quadratic program qp which always has a solution and a high order correction direction is yielded via a system of linear equations sle to avoid the maratos effect after finite iterations the iteration point always get into the feasible set by introducing a new non monotone curve search under some mild conditions including the weak mangasarian fromovitz constraint qualification mfcq the proposed algorithm possesses global convergence and the superlinear convergence is obtained without the strict complementarity finally some elementary numerical experiments are implemented and reported

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

condor a new parallel constrained extension of powell s uobyqa algorithm experimental results and comparison with the dfo algorithm this paper presents an algorithmic extension of powell s uobyqa algorithm unconstrained optimization by quadratical approximation we start by summarizing the original algorithm of powell and by presenting it in a more comprehensible form thereafter we report comparative numerical results between uobyqa dfo and a parallel constrained extension of uobyqa that will be called in the paper condor constrained non linear direct parallel optimization using trust region method for high computing load function the experimental results are very encouraging and validate the approach they open wide possibilities in the field of noisy and high computing load objective functions optimization from 2 min to several days like for instance industrial shape optimization based on computation fluid dynamic codes or partial differential equations solvers finally we present a new easily comprehensible and fully stand alone implementation in c of the parallel algorithm

fully parametric and semi parametric regression models for common events with covariate measurement error in main study validation study designs the derivation of the likelihood function for binary data from two types of main study validation study designs where model covariates are measured with error is elaborated rather than limiting consideration to a restricted family of models with convenient mathematical properties we suggest that empirical considerations customized to the data at hand should drive model choices the joint likelihood function for the main study in which the covariates are measured with error and the validation study in which they are not is maximized and estimation and inference proceeds using standard theory although the choice of the measurement error model is driven by empirical considerations the relatively small validation study sizes typically seen may lead to misspecification resulting in bias in estimation and inference about exposure disease relationships by using a nonparametric form for the measurement error model the resulting semi parametric methods suggested by robins rotnitzky and zhao 1994 journal of the american statistical association 89 864 866 and robins hsieh and newey 1995 journal of the royal statistical society series b 57 409 424 are free from bias due to misspecification of the measurement error model trading efficiency for robustness as usual these fully and semi parametric methods are illustrated with a detailed example from a main study validation study of the health effects of occupational exposure to chemotherapeutics among pharmacists valanis et al 1993 american journal of hospital pharmacy 50 455 462 a constant prevalence ratio model for common binary events with gamma covariate measurement error is derived and empirically verified by the available data a careful reanalysis of the data taking measurement error fully into account leads to a threefold increase in the log relative risk and no loss of statistical power the semi parametric estimates are consistent with the parametric results providing reassurance that important bias due to misspecification of the measurement error model is unlikely

comments on an o n parallel multiplier with bit sequential input and output for the realization of a bit sequential multiplier with operands of length n chen and willoner1 suggest a circuitry consisting of 2n identical modules it is shown that if a slightly different arrangement of the modules is taken the number of modules is reduced to n furthermore the implementation in circuit form can be made more simple

controllability of semilinear boundary problems with nonlocal initial conditions the main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions we show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary the included application to a size structured population equation provides a motivation for abstract results

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

generalized monotone line search sqp algorithm for constrained minimax problems in this article non linear minimax problems with general constraints are discussed by means of solving one quadratic programming an improved direction is yielded and a second order correction direction can also be at hand via one system of linear equations so a new algorithm for solving the discussed problems is presented in connection with a special merit function the generalized monotone line search is used to yield the step size at each iteration under mild conditions we can ensure global and superlinear convergence finally some numerical experiments are operated to test our algorithm and the results demonstrate that it is promising

an sqp feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity in this paper a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed and a new sqp feasible descent algorithm for solving the problems is presented at each iteration of the new algorithm a convex quadratic program qp which always has feasible solution is solved and a master direction is obtained then an improved feasible descent direction is yielded by updating the master direction with an explicit formula and in order to avoid the maratos effect a height order correction direction is computed by another explicit formula of the master direction and the improved direction the new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity furthermore the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted finally some numerical tests are reported

canonical coordinates method for equality constrained nonlinear optimization feasible points methods have several appealing advantages over the infeasible points methods for solving equality constrained nonlinear optimization problems the known feasible points methods however solve often large systems of nonlinear constraint equations in each step in order to maintain feasibility solving nonlinear equations in each step not only slows down the algorithms considerably but also the large amount of floating point computation involved introduces considerable numerical inaccuracy into the overall computation as a result the commercial software packages for equality constrained optimization are slow and not numerically robust we present a radically new approach to maintaining feasibility called the canonical coordinates method ccm the ccm unlike previous methods does not adhere to the coordinate system used in the problem specification rather as the algorithm progresses ccm dynamically chooses in each step a coordinate system that is most appropriate for describing the local geometry around the current iterate by dynamically changing the coordinate system to suit the local geometry the ccm is able to maintain feasibility in equality constrained nonlinear optimization without having to solve systems of nonlinear equations we describe the ccm and present a proof of its convergence we also present a few numerical examples which show that ccm can solve in very few iterations problems that cannot be solved using the commercial nlp solver in matlab 6 1

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

sequential quadratically constrained quadratic programming norm relaxed algorithm of strongly sub feasible directions abstract in this paper we present a sequential quadratically constrained quadratic programming sqcqp norm relaxed algorithm of strongly sub feasible directions for the solution of inequality constrained optimization problems by introducing a new unified line search and making use of the idea of strongly sub feasible direction method the proposed algorithm can well combine the phase of finding a feasible point by finite iterations and the phase of a feasible descent norm relaxed sqcqp algorithm moreover the former phase can preserve the sub feasibility of the current iteration and control the increase of the objective function at each iteration only a consistent convex quadratically constrained quadratic programming problem needs to be solved to obtain a search direction without any other correctional directions the global superlinear and a certain quadratic convergence which is between 1 step and 2 step quadratic convergence properties are proved under reasonable assumptions finally some preliminary numerical results show that the proposed algorithm is also encouraging

a superlinearly convergent norm relaxed sqp method of strongly sub feasible directions for constrained optimization without strict complementarity in this paper a kind of optimization problems with nonlinear inequality constraints is discussed combined the ideas of norm relaxed sqp method and strongly sub feasible direction method as well as a pivoting operation a new fast algorithm with arbitrary initial point for the discussed problem is presented at each iteration of the algorithm an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution and to avoid the maratos effect another correction direction is yielded by a simple explicit formula since the line search technique can automatically combine the initialization and optimization processes after finite iterations the iteration points always get into the feasible set the proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity finally some numerical tests are reported

avoiding the maratos effect by means of a nonmonotone line search ii inequality constrained problems feasible iterates when solving inequality constrained optimization problems via sequential quadratic programming sqp it is potentially advantageous to generate iterates that all satisfy the constraints all quadratic programs encountered are then feasible and there is no need for a surrogate merit function 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 defined outside the feasible set it has recently been shown that this is indeed possible by means of a suitable perturbation of the original sqp iteration without losing superlinear convergence in this context the well known maratos effect is compounded by the possible infeasibility of the full step of one even close to a solution these difficulties have been accommodated by making use of a suitable modification of a bending technique proposed by mayne and polak requiring evaluation of the constraints function at an auxiliary point at each iteration in part i

a generalization of the norm relaxed method of feasible directions this paper generalizes the norm relaxed method of feasible directions which has roots in the classical method of feasible directions mfd this generalized algorithm introduces some parameters which can be adjusted to speed up the convergence an investigation of its global convergence is included and the numerical performance is shown on 15 test problems its global convergence is guaranteed under a rather mild and standard assumption the numerical tests show that this new algorithm converges faster than the previous norm relaxed mfd for most test problems by selecting a set of suitable parameters even though it only has the same guaranteed convergence rate as the previous norm relaxed mfd

a feasible trust region sequential quadratic programming algorithm an algorithm for smooth nonlinear constrained optimization problems is described in which a sequence of feasible iterates is generated by solving a trust region sequential quadratic programming sqp subproblem at each iteration and by perturbing the resulting step to retain feasibility of each iterate by retaining feasibility the algorithm avoids several complications of other trust region sqp approaches the objective function can be used as a merit function and the sqp subproblems are feasible for all choices of the trust region radius global convergence properties are analyzed under various assumptions on the approximate hessian under additional assumptions superlinear convergence to points satisfying second order sufficient conditions is proved

a globally and superlinearly convergent feasible qp free method for nonlinear programming in this paper we propose a qp free type algorithm which solves the problem of minimizing a smooth function subject to smooth inequality constraints in contrast with the sqp methods each iteration this algorithm only needs to solve systems of linear equations which are derived from the equality part in the kkt first order optimality conditions it is observed that if the quasi newton direction is zero we can obtain a direction of descent by dropping a constraint from the active set at the current iterate a high order modified direction is introduced in order to prevent maratos effect global and superlinear convergence are proven under some suitable conditions

domain element method for aerodynamic shape optimization applied to a modern transport wing generic wraparound aerodynamic shape optimization technology is presented and applied to a modern commercial aircraft wing in transonic cruise the wing geometry is parameterized by a novel domain element method which uses efficient global interpolation functions to deform both the surface geometry and corresponding computational fluid dynamics volume mesh the technique also provides a method that allows geometries to be parameterized at various levels ranging from global three dimensional planform alterations to detailed local surface changes combining all levels of parameterization allows for free form design control with very few design variables the method provides an efficient combined shape parameterization and high quality mesh deformation technique that is totally independent of mesh type structured or unstructured optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient based optimizer by finite differences the entire optimization suite has also been parallelized to allow optimization with highly flexible parameterization in practical times results are presented for highly constrained optimizations of the modern aircraft wing in transonic cruise using three levels of parameterization number of design variables to assess the effect of parameterization level on the optimization the highest level optimization results in a totally shock free geometry with an associated substantial reduction in drag

controllability of sobolev type integrodifferential systems in banach spaces sufficient conditions for controllability of sobolev type integrodifferential systems in banach spaces are established the results are obtained using compact semigroups and the schauder fixed point theorem as an example is provided to illustrate the results

a variant of sqp method for inequality constrained optimization and its global convergence in this paper a variant of sqp method for solving inequality constrained optimization is presented this method uses a modified qp subproblem to generate a descent direction as each iteration and can overcome the possible difficulties that the qp subproblem of the standard sqp method is inconsistency furthermore the method can start with an infeasible initial point under mild conditions we prove that the algorithm either terminates as kkt point within finite steps or generates an infinite sequence whose accumulation point is a kkt point or satisfies certain first order necessary condition finally preliminary numerical results are reported

a superlinearly convergent sqp method without boundedness assumptions on any of the iterative sequences this paper is aimed to present a new sequential quadratic programming sqp algorithm for finding a solution to nonlinear constrained programming problems with weak conditions where the improved direction can be yielded by solving one quadratic programming qp and the correction direction can be obtained by solving another qp the main characters of the proposed algorithm are as follows first by limiting infeasibility of sqp iterates the boundedness of the iteration sequence can be obtained in the case of the feasible set being nonempty and bounded as well as the constraint functions being convex second global convergence can be proved under slater constraint qualification cq furthermore superlinear convergence can be ensured under suitable conditions third the proposed algorithm is further improved with a bidirectional line search technique finally some numerical experiments are operated to test the proposed algorithms and the results demonstrate that they are promising

bit serial multipliers and squarers traditional bit serial multipliers present one or more clock cycles of data latency in some situations it is desirable to obtain the output after only a combinational delay as in serial adders and subtracters a serial multiplier and a squarer with no latency cycles are presented here both accept unsigned or sign extended two s complement numbers and produce an arbitrarily long output they are fully modular and thus good candidates for introduction in vlsi libraries

a parametric procedure for ultrametric tree estimation from conditional rank order proximity data the psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models e g hierarchical or ultrametric trees for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures i e procedures which optimize a stress based criteria of fit and whose solutions are invariant under a monotone transformation of the input data this paper proposes a new parametric maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data we present the technical aspects of the model and the estimation algorithm some preliminary monte carlo results are discussed a consumer psychology application is provided examining the similarity of fifteen types of snack breakfast items finally some directions for future research are provided

least squares estimation techniques for position tracking of radioactive sources this paper describes least squares estimation algorithms used for tracking the physical location of radioactive sources in real time as they are moved around in a facility we present both recursive and moving horizon nonlinear least squares estimation algorithms that consider both the change in the source location and the deviation between measurements and model predictions the measurements used to estimate position consist of four count rates reported by four different gamma ray detectors there is an uncertainty in the source location due to the large variance of the detected count rate and the uncertainty in the background count rate this work represents part of a suite of tools which will partially automate security and safety assessments allow some assessments to be done remotely and provide additional sensor modalities with which to make assessments

a feasible sqp method for nonlinear programming in this paper a new sqp algorithm is presented to solve the general nonlinear programs with mixed equality and inequality constraints quoted from p spellucci see 9 this method maybe be named sequential equality constrained quadratic programming secqp algorithm per single iteration based on an active set strategy see 9 this secqp algorithm requires only to solve equality constrained quadratic programming subproblems or system of linear equations the theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions

a new sqp method of feasible directions for nonlinear programming in this paper a new sequential quadratic programming sqp method of feasible directions is proposed and analyzed for nonlinear programming where a feasible direction of descent can be derived from solving only one qp subproblem in particular this method can produce automatically a revised direction with the explicit expression which can avoid maratos effect without solving qp subproblem the theoretical analysis shows that global and superlinear convergence can be induced in the end numerical experiment is given to illustrate the effectiveness of the method

a method combining norm relaxed qp subproblems with systems of linear equations for constrained optimization based on the ideas of norm relaxed sequential quadratic programming sqp method and the strongly sub feasible direction method we propose a new sqp algorithm for the solution of nonlinear inequality constrained optimization unlike the previous work at each iteration the norm relaxed quadratic programming subproblem nrqps in our algorithm only consists of the constraints corresponding to an estimate of the active set and the high order correction direction used to avoid the maratos effect is obtained by solving a system of linear equations sle which also only consists of such a subset of constraints and gradients moreover the line search technique can effectively combine the initialization process with the optimization process and therefore if the starting point is not feasible the iteration points always get into the feasible set after a finite number of iterations the global convergence is proved under the mangasarian fromovitz constraint qualification mfcq and the superlinear convergence is obtained without assuming the strict complementarity finally the numerical experiments show that the proposed algorithm is effective and promising for the test problems

comments on a signed bit sequential multiplier by t rhyne and n r strader ii with reference to the above mentioned paper see ibid vol c 35 p 896 901 1986 it is stated that the authors introduction in which they claim that the references all deal with algorithms for processing unsigned operands is erroneous one of their references most certainly does not deal with unsigned operands as a two s complement number system is one of the module interfacing conventions germane to r lyon s 1981 methodology moreover in the authors conclusions they state that they have now extended bit sequential multiplication to signed two s complement binary operands which may give the doubtless unintended impression that this has not been done before

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

corrigendum on the constant positive linear dependence condition and its application to sqp methods we correct an assertion in the quoted paper qi and wei siam j optim 10 2000 pp 963 981

boundary control problems with nonlinear state equation first order necessary conditions of optimality are obtained for boundary control problems governed by parabolic equations with nonlinear boundary value conditions

a sequential equality constrained quadratic programming algorithm for inequality constrained optimization in this paper the feasible type sqp method is improved a new sqp algorithm is presented to solve the nonlinear inequality constrained optimization as compared with the existing sqp methods per single iteration in order to obtain the search direction it is only necessary to solve equality constrained quadratic programming subproblems and systems of linear equations under some suitable conditions the global and superlinear convergence can be induced

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 type of efficient feasible sqp algorithms for inequality constrained optimization in this paper motivated by zhu et al methods z b zhu k c zhang j b jian an improved sqp algorithm for inequality constrained optimization math meth oper res 58 2003 271 282 zhibin zhu jinbao jian an efficient feasible sqp algorithm for inequality constrained optimization nonlinear anal real world appl 10 2 2009 1220 1228 we propose a type of efficient feasible sqp algorithms to solve nonlinear inequality constrained optimization problems by solving only one qp subproblem with a subset of the constraints estimated as active a class of revised feasible descent directions are generated per single iteration these methods are implementable and globally convergent we also prove that the algorithms have superlinear convergence rate under some mild conditions