Above are papers related to the following paper: [Paper_ID] Paper #312409. 	[Title] A SUCCESSIVE LINEAR PROGRAMMING APPROACH FOR INITIALIZATION AND REINITIALIZATION AFTER DISCONTINUITIES OF DIFFERENTIAL ALGEBRAIC EQUATIONS [Abstract] Determination of consistent initial conditions is an important aspect of the solution of differential algebraic equations (DAEs). Specification of inconsistent initial conditions, even if they are slightly inconsistent, often leads to a failure in the initialization problem. In this paper, we present a Successive Linear Programming (SLP) approach for the solution of the DAE derivative array equations for the initialization problem. The SLP formulation handles roundoff errors and inconsistent user specifications among others and allows for reliable convergence strategies that incorporate variable bounds and trust region concepts. A new consistent set of initial conditions is obtained by minimizing the deviation of the variable values from the specified ones. For problems with discontinuities caused by a step change in the input functions, a new criterion is presented for identifying the subset of variables which are continuous across the discontinuity. The LP formulation is then applied to determine a consistent set of initial conditions for further solution of the problem in the domain after the discontinuity. Numerous example problems are solved to illustrate these concepts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #14083. 	[Title] Data Reconciliation and Gross Error Detection for Dynamic Systems [Abstract] Gross error detection plays a vital role in parameter estimation and data reconciliation for both dynamic and steady state systems. In particular, recent advances in process optimization now allow data reconciliation of dynamic systems and appropriate problem formulations need to be considered for them. Data errors due to either miscalibrated or faulty sensors or just random events nonrepresentative of the underlying statistical distribution, can induce heavy biases in the parameter estimates and in the reconciled data. In this paper we concentrate on robust estimators and exploratory statistical methods which allow us to detect the gross errors as the data reconciliation is performed. These robust methods have the property of being insensitive to departures from ideal statistical distributions and therefore are insensitive to the presence of outliers. Once the regression is done, the outliers can be detected readily by using exploratory statistical techniques. An important feature for performance of the optimization algorithm and uniqueness of the reconciled data is the ability to classify the variables according to their observability and redundancy properties. Here an observable variable is an unmeasured quantity which can be estimated from the measured variables through the physical model while a nonredundant variable is a measured variable which cannot be estimated other than through its measurements. Variable classification can be used as an aid to design instrumentation schemes. In this Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #62676. 	[Title] Nonsmooth Dynamic Simulation With Linear Programming Based Methods [Abstract] Process simulation has emerged as a valuable tool for process design, analysis and operation. In this work, we extend the capabilities of iterated linear programming (LP) for dealing with problems encountered in dynamic nonsmooth process simulation. A previously developed LP method is refined with the addition of a new descent strategy which combines line search with a trust region approach. This adds more stability and efficiency to the method. The LP method has the advantage of naturally dealing with profile bounds as well. This is demonstrated to avoid the computational difficulties which arise from the iterates going into physically unrealistic regions. A new method for the treatment of discontinuities occurring in dynamic simulation problems is also presented in this paper. The method ensures that any event which has occurred within the time interval in consideration is detected and if more than one event occurs, the detected one is indeed the earliest one. A specific class of implicitly discontinuous process simulation problems, phase equilibrium calculations is also looked at. A new formulation is introduced to solve multiphase problems. fl To whom all correspondence should be addressed. email:biegler@cmu.edu Please summarise all the given information.

Paper #312409 has the title `A SUCCESSIVE LINEAR PROGRAMMING APPROACH FOR INITIALIZATION AND REINITIALIZATION AFTER DISCONTINUITIES OF DIFFERENTIAL ALGEBRAIC EQUATIONS  
` and the abstract `Determination of consistent initial conditions is an important aspect of the solution of differential algebraic equations (DAEs). Specification of inconsistent initial conditions, even if they are slightly inconsistent, often leads to a failure in the initialization problem. In this paper, we present a Successive Linear Programming (SLP) approach for the solution of the DAE derivative array equations for the initialization problem. The SLP formulation handles roundoff errors and inconsistent user specifications among others and allows for reliable convergence strategies that incorporate variable bounds and trust region concepts. A new consistent set of initial conditions is obtained by minimizing the deviation of the variable values from the specified ones. For problems with discontinuities caused by a step change in the input functions, a new criterion is presented for identifying the subset of variables which are continuous across the discontinuity. The LP formulation is then applied to determine a consistent set of initial conditions for further solution of the problem in the domain after the discontinuity. Numerous example problems are solved to illustrate these concepts. 
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Question: Which category should Paper #312409 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #312409 has the title `A SUCCESSIVE LINEAR PROGRAMMING APPROACH FOR INITIALIZATION AND REINITIALIZATION AFTER DISCONTINUITIES OF DIFFERENTIAL ALGEBRAIC EQUATIONS  
` and the abstract `Determination of consistent initial conditions is an important aspect of the solution of differential algebraic equations (DAEs). Specification of inconsistent initial conditions, even if they are slightly inconsistent, often leads to a failure in the initialization problem. In this paper, we present a Successive Linear Programming (SLP) approach for the solution of the DAE derivative array equations for the initialization problem. The SLP formulation handles roundoff errors and inconsistent user specifications among others and allows for reliable convergence strategies that incorporate variable bounds and trust region concepts. A new consistent set of initial conditions is obtained by minimizing the deviation of the variable values from the specified ones. For problems with discontinuities caused by a step change in the input functions, a new criterion is presented for identifying the subset of variables which are continuous across the discontinuity. The LP formulation is then applied to determine a consistent set of initial conditions for further solution of the problem in the domain after the discontinuity. Numerous example problems are solved to illustrate these concepts. 
`.
Question: Which category should Paper #312409 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks