Nonlinear Programming (nonlinear + programming)

Distribution by Scientific Domains

Terms modified by Nonlinear Programming

  • nonlinear programming problem

  • Selected Abstracts

    Hyperbolic Penalty: A New Method for Nonlinear Programming with Inequalities

    Adilson Elias Xavier
    This work intends to present and to analyze a new penalty method that purposes to solve the general nonlinear programming problem subject to inequality constraints. The proposed method has the important feature of being completely differentiable and combines features of both exterior and interior penalty methods. Numerical results for some problems are commented on. [source]

    Analog circuit design by nonconvex polynomial optimization: Two design examples

    Siu-Hong Lui
    Abstract We present a framework for synthesizing low-power analog circuits through global optimization over generally nonconvex multivariate polynomial objective function and constraints. Specifically, a nonconvex optimization problem is formed, which is then efficiently solved through convex programming techniques based on linear matrix inequality (LMI) relaxation. The framework allows both polynomial inequality and equality constraints, thereby facilitating more accurate device modelings and parameter tuning. Compared to traditional nonlinear programming (NLP), the proposed methodology exhibits superior computational efficiency, and guarantees convergence to a globally optimal solution. As in other physical design tasks, circuit knowledge and insight are critical for initial problem formulation, while the nonconvex optimization machinery provides a versatile tool and systematic way to locate the optimal parameters meeting design specifications. Two circuit design examples are given, namely, a nested transconductance(Gm),capacitance compensation (NGCC) amplifier and a delta,sigma (,,) analog-to-digital converter (ADC), both of them being the key components in many electronic systems. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Power generation expansion planning with emission control: a nonlinear model and a GA-based heuristic approach

    Jiraporn Sirikum
    Abstract This paper presents an application of genetic algorithms (GA) for solving the long-term power generation expansion planning (PGEP) problem, a highly constrained nonlinear discrete optimization problem. The problem is formulated into a mixed integer nonlinear programming (MINLP) program that determines the most economical investment plan for additional thermal power generating units over a planning horizon, subject to the requirements of power demands, power capacities, loss of load probability (LOLP) levels, locations, and environmental limitations. Computational results show that the GA-based heuristic method can solve the PGEP problem effectively and more efficiently at a significant saving in runtime, when compared with a commercial optimization package. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Tracking control for sampled-data systems with uncertain time-varying sampling intervals and delays

    N. van de Wouw
    Abstract In this paper, a solution to the approximate tracking problem of sampled-data systems with uncertain, time-varying sampling intervals and delays is presented. Such time-varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time-varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input-to-state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete-time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady-state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    An efficient nonlinear programming strategy for PCA models with incomplete data sets

    Rodrigo López-Negrete de la Fuente
    Abstract Processing plants can produce large amounts of data that process engineers use for analysis, monitoring, or control. Principal component analysis (PCA) is well suited to analyze large amounts of (possibly) correlated data, and for reducing the dimensionality of the variable space. Failing online sensors, lost historical data, or missing experiments can lead to data sets that have missing values where the current methods for obtaining the PCA model parameters may give questionable results due to the properties of the estimated parameters. This paper proposes a method based on nonlinear programming (NLP) techniques to obtain the parameters of PCA models in the presence of incomplete data sets. We show the relationship that exists between the nonlinear iterative partial least squares (NIPALS) algorithm and the optimality conditions of the squared residuals minimization problem, and how this leads to the modified NIPALS used for the missing value problem. Moreover, we compare the current NIPALS-based methods with the proposed NLP with a simulation example and an industrial case study, and show how the latter is better suited when there are large amounts of missing values. The solutions obtained with the NLP and the iterative algorithm (IA) are very similar. However when using the NLP-based method, the loadings and scores are guaranteed to be orthogonal, and the scores will have zero mean. The latter is emphasized in the industrial case study. Also, with the industrial data used here we are able to show that the models obtained with the NLP were easier to interpret. Moreover, when using the NLP many fewer iterations were required to obtain them. Copyright © 2010 John Wiley & Sons, Ltd. [source]

    Stochastic mixed integer nonlinear programming using rank filter and ordinal optimization

    AICHE JOURNAL, Issue 11 2009
    Chengtao Wen
    Abstract A rank filter algorithm is developed to cope with the computational-difficulty in solving stochastic mixed integer nonlinear programming (SMINLP) problems. The proposed approximation method estimates the expected performance values, whose relative rank forms a subset of good solutions with high probability. Suboptimal solutions are obtained by searching the subset using the accurate performances. High-computational efficiency is achieved, because the accurate performance is limited to a small subset of the search space. Three benchmark problems show that the rank filter algorithm can reduce computational expense by several orders of magnitude without significant loss of precision. The rank filter algorithm presents an efficient approach for solving the large-scale SMINLP problems that are nonconvex, highly combinatorial, and strongly nonlinear. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

    Dynamic optimization of the methylmethacrylate cell-cast process for plastic sheet production

    AICHE JOURNAL, Issue 6 2009
    Martín Rivera-Toledo
    Abstract Traditionally, the methylmethacrylate (MMA) polymerization reaction process for plastic sheet production has been carried out using warming baths. However, it has been observed that the manufactured polymer tends to feature poor homogeneity characteristics measured in terms of properties like molecular weight distribution. Nonhomogeneous polymer properties should be avoided because they give rise to a product with undesired wide quality characteristics. To improve homogeneity properties force-circulated warm air reactors have been proposed, such reactors are normally operated under isothermal air temperature conditions. However, we demonstrate that dynamic optimal warming temperature profiles lead to a polymer sheet with better homogeneity characteristics, especially when compared against simple isothermal operating policies. In this work, the dynamic optimization of a heating and polymerization reaction process for plastic sheet production in a force-circulated warm air reactor is addressed. The optimization formulation is based on the dynamic representation of the two-directional heating and reaction process taking place within the system, and includes kinetic equations for the bulk free radical polymerization reactions of MMA. The mathematical model is cast as a time dependent partial differential equation (PDE) system, the optimal heating profile calculation turns out to be a dynamic optimization problem embedded in a distributed parameter system. A simultaneous optimization approach is selected to solve the dynamic optimization problem. Trough full discretization of all decision variables, a nonlinear programming (NLP) model is obtained and solved by using the IPOPT optimization solver. The results are presented about the dynamic optimization for two plastic sheets of different thickness and compared them against simple operating policies. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

    Optimal synthesis of p -xylene separation processes based on crystallization technology

    AICHE JOURNAL, Issue 2 2009
    Ricardo M. Lima
    Abstract This article addresses the synthesis and optimization of crystallization processes for p-xylene recovery for systems with feed streams of high concentration, a case that arises in hybrid designs where the first step is commonly performed by adsorption. A novel superstructure and its corresponding mixed-integer nonlinear programming (MINLP) model are proposed. The distinct feature of this superstructure is the capability to generate optimum or near optimum flow sheets for a wide range of specifications of p-xylene compositions in the feed stream of the process. To cope with the complexity of the MINLP model, a two-level decomposition approach, consisting of the solution of an aggregated model and a detailed model, is proposed. The results obtained show good performance of the decomposition strategy, and the optimal flow sheets and p-xylene recoveries are in agreement with the results reported in patents. © 2008 American Institute of Chemical Engineers AIChE J, 2009 [source]

    Operational modeling of multistream heat exchangers with phase changes

    AICHE JOURNAL, Issue 1 2009
    M. M. Faruque Hasan
    Abstract Multistream heat exchangers (MSHE) enable the simultaneous exchange of heat among multiple streams, and are preferred in cryogenic processes such as air separation and LNG. Most MSHEs are complex; proprietary and involve phase changes of mixtures. Although modeling MSHE is crucial for process optimization, no such work exists to our knowledge. We present a novel approach for deriving an approximate operational (vs. design) model from historic data for an MSHE. Using a superstructure of simple 2-stream exchangers, we propose a mixed-integer nonlinear programming (MINLP) formulation to obtain a HE network that best represents the MSHE operation. We also develop an iterative algorithm to solve the large and nonconvex MINLP model in reasonable time, as existing commercial solvers fail to do so. Finally, we demonstrate the application of our work on an MSHE from an existing LNG plant, and successfully predict its performance over a variety of seasons and feed conditions. © 2008 American Institute of Chemical Engineers AIChE J, 2009 [source]

    Optimal carbon source switching strategy for the production of PHA copolymers

    AICHE JOURNAL, Issue 3 2001
    Nikolaos V. Mantzaris
    During polymerization in a nongrowing cell population of Ralstonia eutropha, alternating between two different carbon sources (fructose and fructose/valeric acid) could lead to the production of block copolymers consisting of blocks of homo-poly-3-hydroxybutyrate (PHB) and polyhydroxybutyrate-co-valerate (PHBV) copolymer. The problem of finding the optimal number of carbon source switches and corresponding switching times that maximize the final concentration of diblock copolymers (PHB-PHBV and PHBV-PHB) was addressed. It was mathematically formulated in the mixed-integer nonlinear programming (MINLP) framework, which allows the decomposition of the original problem into the primal and master problems. The primal problem corresponds to the original problem for a fixed number of carbon source switches, whereas the master problem consists of finding the number of carbon source switches that maximizes the optimum solutions of all possible primal problems. The global optimum was obtained for 39 carbon source switches. It corresponds to a mass fraction of 50.6% of final diblock copolymer concentration over the final total polymer concentration. [source]

    Optimal switchover times between two activities utilizing the same resource

    M. Karakul
    Abstract The "gold-mining" decision problem is concerned with the efficient utilization of a delicate mining equipment working in a number of different mines. Richard Bellman was the first to consider this type of a problem. The solution found by Bellman for the finite-horizon, continuous-time version of the problem with two mines is not overly realistic since he assumed that fractional parts of the same mining equipment could be used in different mines and this fraction could change instantaneously. In this paper, we provide some extensions to this model in order to produce more operational and realistic solutions. Our first model is concerned with developing an operational policy where the equipment may be switched from one mine to the other at most once during a finite horizon. In the next extension we incorporate a cost component in the objective function and assume that the horizon length is not fixed but it is the second decision variable. Structural properties of the optimal solutions are obtained using nonlinear programming. Each model and its solution is illustrated with a numerical example. The models developed here may have potential applications in other areas including production of items requiring the same machine or choosing a sequence of activities requiring the same resource. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 186,203, 2002; DOI 10.1002/nav.10008 [source]

    Particle swarm optimization algorithm for constrained problems

    Jian-Ming Zhang
    Abstract A novel particle swarm optimization (PSO) algorithm with the evaluation of infeasibility degree (IFD) of constraints is presented for nonlinear programming (NLP) problems with equality and inequality constraints. The IFD of constraints is defined as the sum of the squared values of the constraint violations. The proposed novel PSO updates the local best position and global best position according to the objective value and the value of IFD simultaneously. The results of several numerical tests and one real engineering optimization problem show that the proposed approach is efficient. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source]