solving multi item lot sizing problems with an mip solver using classification and reformulation based on research on the polyhedral structure of lot sizing models over the last 20 years we claim that there is a nontrivial fraction of practical lot sizing problems that can now be solved by nonspecialists just by taking an appropriate a priori reformulation of the problem and then feeding the resulting formulation into a commercial mixed integer programming solver this claim uses the fact that many multi item problems decompose naturally into a set of single item problems with linking constraints and that there is now a large body of knowledge about single item problems to put this knowledge to use we propose a classification of lot sizing problems in large part single item and then indicate in a set of tables what is known about a particular problem class and how useful it might be specifically we indicate for each class i whether a tight extended formulation is known and its size ii whether one or more families of valid inequalities are known defining the convex hull of solutions and the complexity of the corresponding separation algorithms and iii the complexity of the corresponding optimization algorithms which would be useful if a column generation or lagrangian relaxation approach was envisaged three distinct multi item lot sizing instances are then presented to demonstrate the approach and comparative computational results are presented finally we also use the classification to point out what appear to be some of the important open questions and challenges

facets and algorithms for capacitated lot sizing the dynamic economic lot sizing model which lies at the core of numerous production planning applications is one of the most highly studied models in all of operations research and yet capacitated multi item versions of this problem remain computationally elusive we study the polyhedral structure of an integer programming formulation of a single item capacitated version of this problem and use these results to develop solution methods for multi item applications in particular we introduce a set of valid inequalities for the problem and show that they define facets of the underlying integer programming polyhedron computational results on several single and multiple product examples show that these inequalities can be used quite effectively to develop an efficient cutting plane branch and bound procedure moreover our results show that in many instances adding certain of these inequalities a priori to the problem formulation and avoiding the generation of cutting planes can be equally effective

facets and reformulations for solving production planning with changeover costs we study a scheduling problem with changeover costs and capacity constraints the problem is np complete and combinatorial algorithms for solving it have not performed well we identify a general class of facets that subsumes as special cases some known facets from the literature we also develop a cutting plane based procedure and reformulation for the problem and we obtain optimal solutions to problem instances with up to 600 integer variables without resorting to branch and bound procedures

a polyhedral study of production ramping we give strong formulations of ramping constraints used to model the maximum change in production level for a generator or machine from one time period to the next and production limits for the two period case we give a complete description of the convex hull of the feasible solutions the two period inequalities can be readily used to strengthen ramping formulations without the need for separation for the general case we define exponential classes of multi period variable upper bound and multi period ramping inequalities and give conditions under which these inequalities define facets of ramping polyhedra finally we present exact polynomial separation algorithms for the inequalities and report computational experiments on using them in a branch and cut algorithm to solve unit commitment problems in power generation

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

feedback controllers for a wind tunnel model involving a delay analytical design and numerical simulation an application of a finite spectrum assignment method for time delay systems to a feedback control of mach number in a wind tunnel is presented the linearized model of mach number control is a system of three state equations with a delay in one of the state variables the proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay the spectrum of the closed loop system is finite and consists of three eigenvalues that can be placed arbitrarily four possible variants of the feedback control law are presented the calculation of feedback coefficients is very simple which makes it possible to update the controller s parameters on line with the changes of the operating point an extensive numerical simulation of the system dynamics and the feedback controllers was done and led to several conclusions in particular a very good settling time under problem constraints has been obtained and several nice features of the proposed feedback controller have been demonstrated

on the capacitated lot sizing and continuous 0 1 knapsack polyhedra abstract we consider the single item capacitated lot sizing problem a well known production planning model that often arises in practical applications and derive new classes of valid inequalities for it we first derive new easily computable valid inequalities for the continuous 0 1 knapsack problem which has been introduced recently and has been shown to provide a useful relaxation of mixed 0 1 integer programs we then show that by studying an appropriate continuous 0 1 knapsack relaxation of the capacitated lot sizing problem it is possible not only to derive new classes of valid inequalities for the capacitated lot sizing problem but also to derive and or strengthen several known classes

continuous state feedback tracking of an uncertain heat diffusion process a spatially distributed form of a second order sliding mode control algorithm is suggested for the feedback control of a heat process subject to unmeasurable sufficiently smooth persistent disturbances of arbitrary shape in order to obtain a continuous control input while retaining similar properties of robustness as those usually endowing the discontinuous control systems a dynamic input extension technique is exploited by adding an integrator at the input side and by applying a discontinuous distributed input to the integrator we present a constructive lyapunov analysis of the closed loop performance that yields simple controller tuning conditions guaranteeing the asymptotic tracking of a sufficiently smooth reference trajectory despite the presence of norm bounded persistent disturbances numerical simulations confirm the effectiveness of the proposed approach

evolution equations driven by a fractional brownian motion abstract in this paper we study nonlinear stochastic evolution equations in a hilbert space driven by a cylindrical fractional brownian motion with hurst parameter h 1 2 and nuclear covariance operator we establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter h this result is applied to stochastic parabolic equation perturbed by a fractional white noise in this case if the coefficients are lipschitz continuous and bounded the existence and uniqueness of a solution holds if h d 4 the proofs of our results combine techniques of fractional calculus with semigroup estimates

solving multi item lot sizing problems using strong cutting planes we consider two classes of multi item lot sizing problems the first is a class of single stage problems involving joint machine capacity constraints and or start up costs and the second is a class of multistage problems with general product structure the problems are solved as mixed integer programs based on i an appropriate choice of the initial problem formulation and ii the addition of cuts which are generated automatically by a mathematical programming system mpsarx our results extend and complement those of karmarkar and schrage 1985 afentakis and gavish 1986 eppen and martin 1987 and van roy and wolsey 1987 a major advantage of this approach is its robustness or flexibility by using just a matrix generator and a mathematical programming system with automatic cut generation routines we can formulate and solve model variants without incurring the costs of adapting an algorithm

new stability and exact observability conditions for semilinear wave equations the problem of estimating the initial state of 1 d wave equations with globally lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers and deriving the upper bound for exact observability time in terms of linear matrix inequalities lmis fridman 2013 in the present paper we generalize this result to n d wave equations on a hypercube this extension includes new lmi based exponential stability conditions for n d wave equations as well as an upper bound on the minimum exact observability time in terms of lmis for 1 d wave equations with locally lipschitz nonlinearities we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements the efficiency of the results is illustrated by numerical examples

lot sizing with constant batches formulation and valid inequalities we consider the classical lot sizing problem with constant production capacities lcc and a variant in which the capacity in each period is an integer multiple of some basic batch size lcb we first show that the classical dynamic program for lcc simplifies for lcb leading to an on2 min n c algorithm where n is the number of periods and c the batch size using this new algorithm we show how to formulate both problems as linear programs with on3 variables and constraints a class of so called k l s i inequalities are described for lcb which capture both the dynamic nature of the problem as well as the capacity aspects for lcb we prove that these inequalities are the only facet defining inequalities of a certain form for lcc we show that these inequalities include all the known classes of valid inequalities finally we discuss several open questions and possible extensions

exponential stabilization for 1 d linear ito type state dependent stochastic parabolic pde systems via static output feedback abstract this paper deals with the problem of exponential stabilization for 1 d linear stochastic parabolic partial differential equation pde systems with state multiplicative noise in the form of ito type a static output feedback sof control scheme is proposed to stabilize the stochastic pde system in a stochastic framework via locally collocated piecewise uniform actuators and sensors the closed loop well posedness analysis is provided by virtue of the semi group theory based on the infinite dimensional infinitesimal operator and lyapunov technique the sof controller design is developed to guarantee the exponential stability of the resulting closed loop system in the mean square sense finally simulation results on a stochastic heat equation are presented to verify the effectiveness of the proposed design method

robust distributed control of quasilinear reaction diffusion equations via infinite dimensional sliding modes abstract this paper investigates the problem of robust tracking control for quasilinear reaction diffusion partial differential equations subject to external unknown perturbations the considered class of equations is quite general and includes classical equations such as the heat equation or the fisher kpp equation as special cases global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite dimensional sliding mode controller extensive simulations support and validate the theoretical results

a study of the lot sizing polytope the lot sizing polytope is a fundamental structure contained in many practical production planning problems here we study this polytope and identify facet defining inequalities that cut off all fractional extreme points of its linear programming relaxation as well as liftings from those facets we give a polynomial time combinatorial separation algorithm for the inequalities when capacities are constant we also report computational experiments on solving the lot sizing problem with varying cost and capacity characteristics

observers and initial state recovering for a class of hyperbolic systems via lyapunov method a b s t r a c t recently the problem of estimating the initial state of some linear infinite dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers ramdani tucsnak and weiss 2010 in the present paper we introduce a direct lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval we first design forward observers and derive linear matrix inequalities lmis for the exponential stability of the estimation errors further we obtain simple finite dimensional conditions in terms of lmis for an upper bound t on the minimal time that guarantees the convergence of the sequence of forward and backward observers on 0 t for the initial state recovering this t represents also an upper bound on the observability time for observation times bigger than t these lmis give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the lyapunov functions in our approach t is found as the minimal dwelling time for the switched exponentially stable forward and backward estimation error systems with the different lyapunov functions liberzon 2003 the efficiency of the results is illustrated by numerical examples 2013 elsevier ltd all rights reserved

the continuous mixing polyhedron we analyze the polyhedral structure of the setspcmix s r z r xr nxz n s r j z j f j j 1 n andp cmix pcmixn s 0 the setp cmix is a natural generalization of the mixing set studied by pochet and wolsey 15 16 and ga nla k and pochet 8 and recently has been introduced by miller and wolsey 12 we introduce a new class of valid inequalities that has proven to be sufficient for describing conv pcmix we give an extended formulation of sizeo n xo n2 variables and constraints and indicate how to separate over conv pcmix ino n3 time finally we show how the mixed integer rounding mir inequalities of nemhauser and wolsey 14 and the mixing inequalities of ga nla k and pochet 8 constitute special cases of the cycle inequalities

exponential stabilization of conservation systems with interior disturbance abstract in this paper we consider the stabilization problem of the conservation systems with interior disturbance employing the idea of sliding mode control we design a nonlinear distributed feedback controller we prove the solvability of the resulted closed loop system by the maximal monotone operator theory further we prove the exponential stability of the closed loop system in particular we prove that the requirement of a classical solution in the lyapunov approach is unnecessary

modelling practical lot sizing problems as mixed integer programs in spite of the remarkable improvements in the quality of general purpose mixed integer programming software the effective solution of a variety of lot sizing problems depends crucially on the development of tight formulations for the special problem features occurring in practice after reviewing some of the basic preprocessing techniques for handling safety stocks and multilevel problems we discuss a variety of aspects arising particularly in small and large bucket time period models such as start ups changeovers minimum batch sizes choice of one or two set ups per period etc a set of applications is described that contains one or more of these special features and some indicative computational results are presented finally to show another technique that is useful a slightly different supply chain application is presented for which the a priori addition of some simple mixed integer inequalities based on aggregation leads to important improvements in the results

data driven h_ infty control for nonlinear distributed parameter systems the data driven h infty control problem of nonlinear distributed parameter systems is considered in this paper an off policy learning method is developed to learn the h infty control policy from real system data rather than the mathematical model first karhunen loeve decomposition is used to compute the empirical eigenfunctions which are then employed to derive a reduced order model rom of slow subsystem based on the singular perturbation theory the h infty control problem is reformulated based on the rom which can be transformed to solve the hamilton jacobi isaacs hji equation theoretically to learn the solution of the hji equation from real system data a data driven off policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved for implementation purpose a neural network nn based action critic structure is developed where a critic nn and two action nns are employed to approximate the value function control and disturbance policies respectively subsequently a least square nn weight tuning rule is derived with the method of weighted residuals finally the developed data driven off policy learning approach is applied to a nonlinear diffusion reaction process and the obtained results demonstrate its effectiveness

dynamic knapsack sets and capacitated lot sizing a dynamic knapsack set is a natural generalization of the 0 1 knapsack set with a continuous variable studied recently for dynamic knapsack sets a large family of facet defining inequalities called dynamic knapsack inequalities are derived by fixing variables to one and then lifting surprisingly such inequalities have the simultaneous lifting property and for small instances provide a significant proportion of all the facet defining inequalities we then consider single item capacitated lot sizing problems and propose the joint study of three related sets the first models the discrete lotsizing problem the second the continuous lot sizing problem with wagnerwhitin costs and the third the continuous lot sizing problem with arbitrary costs the first set that arises is precisely a dynamic knapsack set the second an intersection of dynamic knapsack sets and the unrestricted problem can be viewed as both a relaxation and a restriction of the second it follows that the dynamic knapsack inequalities and their generalizations provide strong valid inequalities for all three sets some limited computation results are reported as an initial test of the effectiveness of these inequalities on capacitated lot sizing problems

d type anticipatory iterative learning control for a class of inhomogeneous heat equations in this paper a d type anticipatory iterative learning control ilc scheme is applied to the boundary control of a class of inhomogeneous heat equations where the heat flux at one side is the control input while the temperature measurement at the other side is the control output by transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded jacobi theta functions the learning convergence of ilc is guaranteed through rigorous analysis without any simplification or discretization of the 3d dynamics in the time space as well as iteration domains the adopted ilc scheme makes full use of the process repetition and deals with state independent or state dependent uncertainties meanwhile due to the feedforward characteristic of ilc the proposed scheme not only makes anticipatory compensation possible to overcome the heat conduction delay in boundary output tracking but also eliminates the gain margin limitation encountered in feedback control in the end an illustrative example is presented to demonstrate the performance of the proposed ilc scheme

polyhedra for lot sizing with wagner whitin costs we examine the single item lot sizing problem with wagner whitin costs over ann period horizon i e pt ht pt 1 fort 1 n 1 wherept ht are the unit production and storage costs in periodt respectively so it always pays to produce as late as possible

the existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion abstract in this paper we investigate the existence uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional brownian motion b q h t d x t a x t f t x t d t g t d b q h t with hurst parameter h 1 2 1 we also consider the existence of weak solutions

exponential stabilization of the uncertain wave equation via distributed dynamic input extension the wave equation is studied under the effect of a persistent external perturbation a dynamical distributed controller is suggested based on an infinite dimensional generalization of second order sliding mode control techniques that provides the exponential attainment of a sufficiently smooth arbitrary reference of the state trajectory the control system comprises of both feedforward and feedback parts the latter being a discontinuous term directly connected to the plant input through a dynamical filter that augments the system state smoothing out the discontinuity of the feedback control loop as a result a continuous input is applied to the plant a constructive lyapunov based proof of convergence of the proposed control algorithm is carried out and supporting numerical results are presented

stability analysis of linear partial differential equations with generalized energy functions we present a method for the stability analysis of a large class of linear partial differential equations pdes in one spatial dimension we rely on lyapunov analysis to establish the exponential stability of the systems under consideration the proposed test for the verification of the underlying lyapunov inequalities relies on the existence of solutions of a system of coupled differential equations we illustrate the application of this method using a pde actuated by a backstepping computed feedback law furthermore for the case of pdes defined by polynomial data we formulate a numerical methodology in the form of a convex optimization problem which can be solved algorithmically we show the effectiveness of the proposed numerical methodology using examples of different types of pdes

exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach this paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations pdes for which a finite number of actuators are used a fuzzy control design methodology is developed for these systems by combining the pde theory and the takagi sugeno t s fuzzy model based control technique initially a t s fuzzy parabolic pde model is proposed to accurately represent a semilinear parabolic pde system then based on the t s fuzzy model a lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a given decay rate the stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities sdlmis furthermore a recursive algorithm is presented to solve the sdlmis via the existing linear matrix inequality optimization techniques finally numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

pointwise exponential stabilization of a linear parabolic pde system using non collocated pointwise observation this paper deals with the problem of exponential stabilization for a linear distributed parameter system dps using pointwise control and non collocated pointwise observation where the system is modeled by a parabolic partial differential equation pde the main objective of this paper is to construct an output feedback controller for pointwise exponential stabilization of the linear parabolic pde system using the non collocated pointwise observation the observer based output feedback control technique is utilized to overcome the design difficulty caused by the non collocation pointwise observation we construct a luenberger type pde state observer to exponentially track the state of the pde system a collocated pointwise feedback controller is proposed based on the estimated state a variation of poincare wirtinger inequality is derived and the spatial domain is decomposed into multiple sub domains according to the number of the actuators and sensors by using lyapunov s direct method integration by parts and the variation of poincare wirtinger inequality at each sub domain sufficient conditions for the existence of the observer based out feedback controller are developed such that the resulting closed loop system is exponentially stable and presented in terms of standard linear matrix inequalities lmis furthermore the closed loop well posedness analysis is also provided by the semigroup approach extensive numerical simulation results are presented to show the performance of the proposed output feedback controller

guaranteed cost design for controlling semilinear parabolic pde systems with mobile collocated actuators and sensors this paper investigates the guaranteed cost design problem for controlling a class of semilinear parabolic partial differential equation pde systems using mobile collocated actuators and sensors

meta heuristics for dynamic lot sizing a review and comparison of solution approaches proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve because these problems are so difficult various solution techniques have been proposed to solve them in the past decade meta heuristics such as tabu search genetic algorithms and simulated annealing have become popular and efficient tools for solving hard combinatorial optimization problems we review the various meta heuristics that have been specifically developed to solve lot sizing problems discussing their main components such as representation evaluation neighborhood definition and genetic operators further we briefly review other solution approaches such as dynamic programming cutting planes dantzig wolfe decomposition lagrange relaxation and dedicated heuristics this allows us to compare these techniques understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms finally we discuss general guidelines for computational experiments and illustrate these with several examples

existence of mild solutions to stochastic neutral partial functional differential equations with non lipschitz coefficients under a non lipschitz condition with the lipschitz condition being considered as a special case and a weakened linear growth condition the existence and uniqueness of mild solutions to stochastic neutral partial functional differential equations snpfdes is investigated some results in govindan 2003 2005 2 6 are generalized to cover a class of more general snpfdes

a heuristic approach for big bucket multi level production planning problems multi level production planning problems in which multiple items compete for the same resources frequently occur in practice yet remain daunting in their difficulty to solve in this paper we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot sizing problems in addition unlike many other heuristics it generates high quality lower bounds using strong formulations and its simple scheme allows it to be easily implemented in the xpress mosel modeling language extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic particularly for challenging problems

almost periodic solutions of neutral functional differential equations in this paper we study a non autonomous neutral functional differential equation in a banach space applying the theory of semigroups of operators to evolution equations and krasnoselskii s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration

a cutting plane approach to capacitated lot sizing with start up costs we consider a mixed integer model for multi item single machine production planning incorporating both start up costs and machine capacity the single item version of this model is studied from the polyhedral point of view and several families of valid inequalities are derived for some of these inequalities we give necessary and sufficient facet inducing conditions and efficient separation algorithms we use these inequalities in a cutting plane branch and bound procedure a set of real life based problems with 5 items and up to 36 periods is solved to optimality

event based control of linear hyperbolic systems of conservation laws in this article we introduce event based boundary controls for 1 dimensional linear hyperbolic systems of conservation laws inspired by event triggered controls developed for finite dimensional systems an extension to the infinite dimensional case by means of lyapunov techniques is studied the main contribution of the paper lies in the definition of two event triggering conditions by which global exponential stability and well posedness of the system under investigation is achieved some numerical simulations are performed for the control of a system describing traffic flow on a roundabout

boundary second order sliding mode control of an uncertain heat process with unbounded matched perturbation the primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation the underlying heat process is governed by an uncertain parabolic partial differential equation pde with neumann boundary conditions it exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance which is not available for measurements and which is possibly unbounded in magnitude the proposed robust synthesis is formed by the linear feedback design and by the twisting second order sliding mode control algorithm suitably combined and re worked in the infinite dimensional setting a non standard lyapunov functional is invoked to establish the global asymptotic stability in a sobolev space involving spatial state derivatives of the same order as that of the plant equation the stability proof is accompanied by a set of simple tuning rules for the controller parameters the effectiveness of the developed control scheme is supported by simulation results

stochastic evolution equations with fractional brownian motion in this paper linear stochastic evolution equations driven by infinite dimensional fractional brownian motion are studied a necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed separate proofs are required for the cases of hurst parameter above and below 1 2 the particular case of the laplacian on the circle is discussed in detail

a strong cutting plane algorithm for production scheduling with changeover costs changeover costs and times are central to numerous manufacturing operations these costs arise whenever work centers capable of processing only one product at a time switch from the manufacture of one product to another although many researchers have contributed to the solution of scheduling problems that include changeover costs due to the problem s combinatorial explosiveness optimization based methods have met with limited success in this paper we develop and apply polyhedral methods from integer programming for a dynamic version of the problem computational tests with problems containing one to five products and up to 225 integer variables show that polyhedral methods based upon a set of facet inequalities developed in this paper can effectively reduce the gap between the value of an integer programming formulation of the problem and its linear programming relaxation by a factor of 94 to 100 these results suggest the use of a combined cutting plane branch and bound procedure as a solution approach in a test with a five product problem this procedure when compared with a standard linear programming based branch and bound approach reduced computation time by a factor of seven

nonlinear functional differential equations of monotone type in hilbert spaces abstract in this paper we study a class of semilinear functional evolution equations with finite delay in which the nonlinearity satisfies the weak condition of demicontinuity with respect to functional variable and also a semimonotone condition we will prove the existence uniqueness and measurability of the mild solutions based on an extension of the analogous results for non delay initial value problems on banach spaces and a version of recently developed random schauder s fixed point theorem this will be done first for the generalized solutions and then we follow an approximating procedure to obtain the same results for the mild solutions

existence and uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to the class of semilinear differential equations of the form u t au t f t bu t where a is the infinitesimal generator of an analytic semigroup acting on a complex banach space x b d b x x is a densely defined closed linear operator and f r x x is a jointly continuous function under some suitable assumptions on a b and f the existence and uniqueness of a pseudoalmost periodic solution to is obtained

on almost periodic mild solutions for neutral stochastic evolution equations with infinite delay abstract in this paper a class of neutral stochastic functional evolution equations with infinite delay is investigated under some suitable assumptions the existence and uniqueness of quadratic mean almost periodic mild solutions for these equations are discussed by means of semigroups of operators and the fixed point method moreover two examples are given to illustrate our results

lot sizing with inventory bounds and fixed costs polyhedral study and computation we investigate the polyhedral structure of the lot sizing problem with inventory bounds we consider two models one with linear cost on inventory the other with linear and fixed costs on inventory for both models we identify facet defining inequalities that make use of the inventory bounds explicitly and give exact separation algorithms we also describe a linear programming formulation of the problem when the order and inventory costs satisfy the wagner whitin nonspeculative property we present computational experiments that show the effectiveness of the results in tightening the linear programming relaxations of the lot sizing problem with inventory bounds and fixed costs

a convex sum of squares approach to analysis state feedback and output feedback control of parabolic pdes we present an optimization based framework for analysis and control of linear parabolic partial differential equations pdes with spatially varying coefficients without discretization or numerical approximation for controller synthesis we consider both full state feedback and point observation output feedback the input occurs at the boundary point actuation we use positive definite matrices to parameterize positive lyapunov functions and polynomials to parameterize controller and observer gains we use duality and an invertible state variable transformation to convexify the controller synthesis problem finally we combine our synthesis condition with the luenberger observer framework to express the output feedback controller synthesis problem as a set of lmi sdp constraints we perform an extensive set of numerical experiments to demonstrate the accuracy of the conditions and to prove the necessity of the lyapunov structures chosen we provide numerical and analytical comparisons with alternative approaches to control including sturm liouville theory and backstepping finally we use numerical tests to show that the method retains its accuracy for alternative boundary conditions