A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear ...
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A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
We present two solution algorithms for a large-scale integrated assessment model of climate change mitigation: the well known Negishi algorithm and a newly developed Nash algorithm. The algorithms are used to calculat...
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We present two solution algorithms for a large-scale integrated assessment model of climate change mitigation: the well known Negishi algorithm and a newly developed Nash algorithm. The algorithms are used to calculate the Pareto-optimum and competitive equilibrium, respectively, for the global model that includes trade in a number of goods as an interaction between regions. We demonstrate that in the absence of externalities both algorithms deliver the same solution. The Nash algorithm is computationally much more effective, and scales more favorably with the number of regions. In the presence of externalities between regions the two solutions differ, which we demonstrate by the inclusion of global spillovers from learning-by-doing in the energy sector. The non-cooperative treatment of the spillover externality in the Nash algorithm leads to a delay in the expansion of renewable energy installations compared to the cooperative solution derived using the Negishi algorithm.
Evaluation of secure bilateral transactions is one of the important functions of system operator to maintain power system security for better planning and operation in open access competitive restructured electricity ...
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Evaluation of secure bilateral transactions is one of the important functions of system operator to maintain power system security for better planning and operation in open access competitive restructured electricity markets. With integration of distributed generation resources, the security issue of bilateral coordinated markets has gained further attention as distributed generation sources can enter into bilateral contracts with distribution companies. This paper proposes a new method for secure bilateral transactions determination in the presence of distributed generation share in bilateral coordinated electricity markets. The secure bilateral transactions have been determined with different share of distributed generation along with the conventional generators. The pattern of secure bilateral transactions for conventional generation, distributed generation, generation share for bilateral demand, and demand pattern have been obtained for pool plus bilateral market model. The proposed technique has been applied on IEEE 24-bus reliability test system (RTS).
A large number of problems in ab-initio quantum chemistry involve finding the global minimum of the total system energy. These problems are traditionally solved by numerical approaches equivalent to local optimization...
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A large number of problems in ab-initio quantum chemistry involve finding the global minimum of the total system energy. These problems are traditionally solved by numerical approaches equivalent to local optimization. While these approaches are relatively efficient, they do not provide guarantees of global optimality unless a starting point sufficiently close to the global minimum is known apriori. Due to the enormous amount of computational effort required to solve these problems, more mathematically rigorous alternatives have so far received very little attention. Taking the above issue into consideration, this paper explores the use of deterministic global optimization in the context of Hartree-Fock theory, an important mathematical model applied in many quantum chemistry methods. In particular, it presents a general purpose approach for generating linear relaxations for problems arising from Hartree-Fock theory. This was then implemented as an extension to the (Convex Over and Under ENvelopes for nonlinear Estimation) branch and bound mixed integer non-linear programs solver. Proof of concept calculations that simultaneously optimise the orbital coefficients and the location of the nuclei in closed-shell Hartree-Fock calculations are presented and discussed.
A selection index which maximizes genetic gains in a desired direction has been previously suggested. We extent this index to the case where desired relative gentic gains are constrained to be not less or not greater ...
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A selection index which maximizes genetic gains in a desired direction has been previously suggested. We extent this index to the case where desired relative gentic gains are constrained to be not less or not greater than pre-specified levels. Further, we suggest an index for desired relative genetic gains constrained to be between certain levels. All these indices are obtained using quadratic programming techniques.
The focus of this paper is on Dutch auctions where the bidding prices are restricted to a finite set of values and the number of bidders follows a Poisson distribution. The goal is to determine what the discrete bid l...
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The focus of this paper is on Dutch auctions where the bidding prices are restricted to a finite set of values and the number of bidders follows a Poisson distribution. The goal is to determine what the discrete bid levels should be to maximize the auctioneer's expected revenue, which is the same as the average selling price of the object under consideration. We take a new approach to the problem by formulating the descending-price competitive bidding process as a nonlinear program. The optimal solution indicates that the interval between two successive bids should be wider as the Dutch auction progresses. Moreover, the auctioneer's maximum expected revenue increases with the number of bid levels to be set as well as the expected number of bidders. Numerical examples are provided to illustrate the key results from this study and their managerial implications are discussed.
We introduce the optimizer CSOLNP, which is a C++ implementation of the R package RSOLNP (Ghalanos & Theussl, 2012, Rsolnp: General non-linear optimization using augmented Lagrange multiplier method. R package ver...
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We introduce the optimizer CSOLNP, which is a C++ implementation of the R package RSOLNP (Ghalanos & Theussl, 2012, Rsolnp: General non-linear optimization using augmented Lagrange multiplier method. R package version, 1) alongside some improvements. CSOLNP solves non-linearly constrained optimization problems using a Sequential Quadratic programming (SQP) algorithm. CSOLNP, NPSOL (a very popular implementation of SQP method in FORTRAN (Gill et al., 1986, User's guide for NPSOL (version 4.0): A Fortran package for nonlinearprogramming (No. SOL-86-2). Stanford, CA: Stanford University Systems Optimization Laboratory), and SLSQP (another SQP implementation available as part of the NLOPT collection (Johnson, 2014, The NLopt nonlinear-optimization package. Retrieved from http://***/nlopt)) are three optimizers available in OpenMx package. These optimizers are compared in terms of runtimes, final objective values, and memory consumption. A Monte Carlo analysis of the performance of the optimizers was performed on ordinal and continuous models with five variables and one or two factors. While the relative difference between the objective values is less than 0.5%, CSOLNP is in general faster than NPSOL and SLSQP for ordinal analysis. As for continuous data, none of the optimizers performs consistently faster than the others. In terms of memory usage, we used Valgrind's heap profiler tool, called Massif, on one-factor threshold models. CSOLNP and NPSOL consume the same amount of memory, while SLSQP uses 71 MB more memory than the other two optimizers.
We consider an EOQ inventory model for growing items, wherein the value and size of items increase during time, some instances of these items are livestock, fish, and poultry. The main difference between this inventor...
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We consider an EOQ inventory model for growing items, wherein the value and size of items increase during time, some instances of these items are livestock, fish, and poultry. The main difference between this inventory system and older ones is weight increment of products during stocking without buying more. This paper studies an inventory system of poultries that new-born items are fed to reach the ideal weight for consumers. In this study, based on the consumers' preference of fresh foods over frozen items, we assume that shortage is permitted and consumers wait for fresh items when company pays some additional penalties, i.e., the shortage is fully backordered. On the other hand, for each cycle, the producer must prepare the place in terms of hygiene conditions;thus, a setup time per cycle is considered. The aim of this study is to obtain optimum system solution, such that total costs, including setup, purchasing, holding, feeding, and shortage, are minimized. To do so, we employ mathematical measures to approximate growing rates and model the system as a non-linear programming. To solve the obtained optimization model, we employ hessian matrix to obtain optimal solution for this inventory system. The proposed EOQ inventory model helps poultry industries in Iran to optimize their system considering costs and permissible shortage, and it can be employed in other countries. Finally, we provide a numerical example and its sensitivity analysis, plus some potential future directions.
We introduce a method which based on Bell inequalities, to study quantum phase transitions. By using the non-linear programming, we compare two different kinds of Bell inequalities, the original Bell inequality and Cl...
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We introduce a method which based on Bell inequalities, to study quantum phase transitions. By using the non-linear programming, we compare two different kinds of Bell inequalities, the original Bell inequality and Clauser-Horne-Shimony-Holt (CHSH) inequality. And we find that the original Bell inequality is more accurate in detecting the Bell non-locality. By defining the maximal violation of Bell inequalities, we calculate two kinds of transitions, the one is magnetic transition in the spin- 1/2 XX model and the other is topological transition in the Kitaev honeycomb model. The critical points are detected successfully. Compared with traditional methods, our method requires no prior knowledge of order parameters and it is base-free.
Averaging methods with closure approximations and perturbative methods have been discussed in control literature. Suggests that continuing mathematical developments in the decomposition method allow a better approach ...
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Averaging methods with closure approximations and perturbative methods have been discussed in control literature. Suggests that continuing mathematical developments in the decomposition method allow a better approach without the disadvantages of the above.
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