a gradient algorithm for chance constrained nonlinear goal programming abstract decision environments involve high degrees of uncertainty as well as multiple conflicting objectives often sampling information is available as a means of describing uncertainty this description can be utilized in the form of chance constraints goal programming offers a means of considering multiple conflicting objectives a nonlinear goal programming algorithm is presented based upon the gradient method utilizing an optimal step length for chance constrained goal programming models the resulting algorithm requires assumptions of convex solution sets differentiable and monotonic nonlinear constraints and normally distributed variance of stochastic parameters the algorithm is evaluated for generality reliability and precision sensitivity to parameters and data preparational and computational effort and convergence model sensitivity to parameters is identified as well as appropriate adjustment the algorithm was found to require minimal preparational effort favorable computation time and rapid convergence to optimal solution with the exception of models containing high degrees of nonlinearity

stabilization of a non linear distributed parameter vibratory system the feedback stabilization problem for a non linear elastic distributed parameter system including a destabilizing effect is studied the model is formulated as an evolution equation in a hilbert space semigroup theory is used to investigate an initial value problem for the equation moreover a control system with a finite dimensional controller is constructed it is then proved that the state of the overall system converges to zero with a desirable exponential decay rate as time tends to infinity

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

on the stabilizability of a structural acoustic model which incorporates shear effects in the structural component abstract in this paper we consider a linear three dimensional structural acoustic model which takes account of displacement rotational inertia and shear effects in the flat flexible structural component of the model thus the deflections of the structural component of the structure are governed by the reissner mindlin plate equations we show strong stabilization of the coupled model without incorporating viscous or boundary damping in the equations for the gas dynamics and without imposing geometric conditions it turns out that damping is needed in the interior of the plate to which end kelvin voigt damping is introduced in the plate equations as our main tool we use a resolvent criterion for strong stability due to tomilov

on multi component ermakov systems in a two layer fluid a variational approach by introducing madelung type transformations a two layer fluid model with a circular paraboloidal bottom topography is reduced to coupled nonlinear schrodinger equations incorporating harmonic traps and de broglie bohm quantum potentials a kind of multi component ermakov system is obtained via a variational approach and a multi parameter gaussian ansatz in particular three typical reductions to generalized ermakov systems are discussed notable integrals of motion and additional hamiltonian structures are employed to derive analytical solutions in terms of elliptic integrals for the multi component ermakov systems

quantum mechanics as a multidimensional ermakov theory i time independent systems presents a multidimensional ermakov theory applicable to both separable and nonseparable time independent quantum mechanical systems the separability of the system being determined by the separability of the wavefunction in configuration space a consequence of the theory is the existence of a new exact invariant for multidimensional quantum systems in one dimension the author shows that this new invariant reduces to the well known ermakov lewis invariant two applications of the theory are given in the first case a new exact invariant is obtained for planar optical and particle channelling systems in the second case he obtains the ermakov invariants and electron ray path equations for the hydrogen atom

genetic algorithm based technique for solving chance constrained problems management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information chance constrained programming ccp have been used for modelling and analysis of risks in a number of application domains however the resulting mathematical problems are non trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non linear non convex and the stochastic nature we develop and implement c classes to represent such ccp problems we propose a framework consisting of genetic algorithm and monte carlo simulation in order to process the problems the non linear and non convex nature of the ccp problems are processed using genetic algorithm whereas the stochastic nature is addressed through simulation the computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems

decision problems under risk and chance constrained programming dilemmas in the transition some important conceptual problems concerning the application of chance constrained programming ccp to risky practical decision problems are discussed by comparing ccp to stochastic programming with recourse spr we expand on garstka s distinction between mathematical equivalence and economic equivalence showing that much of practical usefulness is lost in the transition between spr and ccp by examining the literature on ccp applications we conclude that there is little evidence that ccp is used with the care that is necessary finally we conclude that ccp is seriously deficient as a modeling technique and of limited value as a computational device

lie symmetries nonlinear equations of motion and new ermakov systems it is shown that a lagrangian of the form l 1 1 rho 2 omega 2 t rho 2 g t f k t rho said to be in factored form yields an equation of motion that is equivalent to the most general equation derivable via noether s theorem from the unfactored lagrangian l 1 2 rho 2 p rho t in view of this equivalence the theory of extended lie groups is applied to the factored nonlinear equation of motion p omega 2 t rho g t f k t rho to obtain its lie symmetries the latter are obtained when g t and k t initially arbitrary are determined in terms of a function x t which satisfies the auxiliary equation x omega 2 t x k x3 it is then possible with the auxiliary equation and the equation of motion to form a coupled pair of nonlinear equations an ermakov system whose first integral is not invariant under the action of the symmetry group in contrast to previous ermakov systems

a linear approximation method for solving a special class of the chance constrained programming problem abstract this article presents a technique which seeks the optimum or near optimum solution of a nonlinear problem by searching through the set of nondominated solutions of the bicriterion linear programming blp problem an approximation formula for constructing two linear objective functions based on the nonlinear objective function of the equivalent deterministic form edf of the stochastic programming model is presented it is proved that a finite number of nondominated solutions need to be investigated before the algorithm converges to the optimum solution point each nondominated solution point is the optimum solution of a linear problem over the feasible region of the nonlinear problem along with an added compromise constraint this compromise constraint is a hyperplane passing through the ideal solution point of the blp problem the most attractive feature of this new practical technique is its ability to search for the optimal solution without examining the whole set of feasible solutions

probabilistic programming for nitrate pollution control comparing different probabilistic constraint approximations abstract agricultural nitrate emissions within a river catchment are due to rainfall and other sources of natural variation uncertain a regulator aiming to reduce nitrate emissions into surface and groundwater faces a trade off between reliability in achieving emission standards and the cost of compliance to agriculture this paper explores this trade off by comparing different assumptions about the probability distribution of nitrate emissions and thus the probabilistic constraint included in the catchment model three categories of probabilistic constraints are considered 1 non parametric 2 normal and 3 lognormal the results indicate that the restrictiveness of the non parametric assumption could lead to a significant reduction in profit relative to the normal and lognormal the lognormal assumption although it is theoretically correct cannot be generalised to the case of correlated emissions however ignoring the dependence between different sources of nitrate emissions introduces more bias than mis specifying their distribution therefore a probabilistic constraint based on a correlated normal distribution of emissions gives the best approximation for nitrate emissions in this study

experimental study on the efficiency and accuracy of a chance constrained programming algorithm abstract the chaps algorithm chaps chance constrained programming system has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other the chaps algorithm is based on the separation linearization and iterative adjusting of linearization of chance constrained deterministic equivalents by using the simplex method according to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance constrained model the positive result is partly due to the fact that the linearized model is very sparse the algorithm requires six to eight chaps iteration runs in order to achieve sufficient accuracy in practice 10 5 10 6 the algorithm converges linearly and its asymptotic error constant is 1 4

uniform stabilization of the dynamic elastica by boundary feedback it is proved that the dynamic elastica which is a nonlinear model describing the large deflecting motion of an inextensible beam can be uniformly exponentially stabilized by boundary velocity feedback

semigroup model and stability of the structurally damped timoshenko beam with boundary inputs abstract this paper is concerned with the linear partial differential equation describing the motion of the timoshenko beam with viscous internal dampings and with a certain type of boundary inputs the equation is formulated as an evolution equation of the form dz t dt az i in a hilbert space and then it is proved for the linear operator a to generate an analytic semigroup moreover the stability of the boundary control system is examined it is shown that in some cases the present type of boundary inputs degrades the degree of stability of the system this is a remarkable contrast to the results of previous research which states that the same type of boundary inputs are effctive in stabilizing the timoshenko beam without any structural damping

stability and periodicity in coupled pinney equations abstract we show that the coupled pinney equations with periodic coefficient constitute a class of nonlinear coupled hill s equations for which the problems of stability and periodicity of the solutions reduce to those for a pair of uncoupled linear hill s equations one of which is of ince type

a cutting plane approach for chance constrained linear programs one approach for solving linear programs with random coefficients is chance constrained programming for the case where the technical coefficients are normally distributed we present a convergent cutting plane algorithm to solve the equivalent nonlinear program which takes advantage of the characteristics of the problem the algorithm requires a moderate computational effort and compares favorably with a general nonlinear code and other approaches proposed for solving this problem

chance constrained programming in activity networks a critical evaluation abstract we review the chance constrained programming ccp model for event realization in activity networks ans and the more recent contribution to it by kress from the points of view of validity and accuracy we present a classification scheme of stochastic programming and confirm that the ccp does not solve the problem of finding a point estimate that satisfies a required confidence level and is of little help in determining the cumulative distribution function c d f of the project completion time we show that the ccp leads to an extremely weak lower bound l b on the exact c d f a backtracking approach is proposed that improves this l b via the ccp which is still too weak to be of any practical value finally we utilize the ccp approach to derive a result due to kress in a simpler and more direct way we also demonstrate that the result itself unfortunately is of questionable validity

an exact invariant for a class of time dependent anharmonic oscillators with cubic anharmonicity an exact invariant is constructed for a class of time dependent anharmonic oscillators using the method of the lie theory of extended groups the presence of the anharmonic term imposes a constraint on the nature of the time dependence for a subclass it is possible to obtain an energy like integral and a condition under which the motion is bounded

on 2 1 dimensional ermakov systems ermakov type systems in 2 1 dimensions are introduced multiwave solutions of a 2 1 dimensional pinney equation and a modulated 2 1 dimensional sine gordon equation are thereby constructed

numerical approach to the non linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems the article is devoted to the analysis of the approximate controllability of a given type of second order infinite dimensional system defined by the hyperbolic type partial differential equation with dirichlet like type zero boundary conditions defined in the n dimensional rectangular prism following this aim spectral theory for linear unbounded operators is involved new numerical algorithms for solving some kind of non linear diofantic equations corresponding with the spectral properties of the unbounded operators are presented and proved an algorithm is optimized for eliminating the symmetrical solutions not interesting in the scope of verification of the controllability next the limit which shows that the direct application of the analytical methods of verifying the controllability in the numerical approach is impossible is proved finally so called partial approximate controllability is defined and the numerical algorithm for its verification is presented finally proven theorems are applied

evaluation of the accuracy of naslund s approximation for managerial decision making under uncertainty abstract this paper uses chance constrained mathematical programming ccp as a tool in project selection when the coefficients involved are independent normal random variables the main contribution of the paper centers around showing how well chance constrained programs can be solved using naslund s approximation instead of other mathematical methods if a given decision process involves a degree of uncertainty in its parameters and only binary decisions are required then it is shown that approximation is the only available solution method

new exactly solvable isospectral partners for symmetric potentials we examine in detail the possibility of applying the darboux transformation to non hermitian hamiltonians in particular we propose a simple method of constructing exactly solvable symmetric potentials by applying darboux transformation to higher states of an exactly solvable symmetric potential it is shown that the resulting hamiltonian and the original one are pseudo supersymmetric partners we also discuss application of the darboux transformation to hamiltonians with spontaneously broken symmetry

lagrangian decomposition of block separable mixed integer all quadratic programs the purpose of this paper is threefold first we propose splitting schemes for reformulating non separable problems as block separable problems second we show that the lagrangian dual of a block separable mixed integer all quadratic program miqqp can be formulated as an eigenvalue optimization problem keeping the block separable structure finally we report numerical results on solving the eigenvalue optimization problem by a proximal bundle algorithm applying lagrangian decomposition the results indicate that appropriate block separable reformulations of miqqps could accelerate the running time of dual solution algorithms considerably

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

controllability of dynamical systems with constraints abstract the article is devoted to analysing the approximate controllability without constrains and constrained controllability with non negative controls of a given type second order infinite dimensional system the considered dynamical system is governed by evolution equation with three damping terms and three terms without derivatives following this aim spectral theory for linear unbounded operators is involved at first remind the representation of considered infinite dimensional dynamical system by the infinite series of finite dimensional systems next two theorems on necessary and sufficient conditions of unconstrained and constrained approximate controllability of considered system are formulated and proved finally proven theorems are applied to two particular dynamical systems including one infinite dimensional