Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Optimization

1975 ◽  
Author(s):  
Leon S. Lasdon ◽  
Allan D. Waren ◽  
Arvind Jain ◽  
Margery W. Ratner
Keyword(s):  
Nonlinear Optimization ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Design And Testing

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

1978 ◽  
Vol 4 (1) ◽  
pp. 34-50 ◽  
Author(s):  
L. S. Lasdon ◽  
A. D. Waren ◽  
A. Jain ◽  
M. Ratner
Keyword(s):  
Nonlinear Programming ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Design And Testing

Optimal Design of a Mechanism Used for Opening and Shutting a Ship’s Hatch Cover

1984 ◽  
Vol 106 (4) ◽  
pp. 503-509
Author(s):  
Koichi Ito ◽  
Tadashi Kuroiwa ◽  
Shinsuke Akagi
Keyword(s):  
Optimal Design ◽  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Numerical Study ◽  
Optimal Solution ◽  
Optimization Method ◽  
Gradient Algorithm ◽  
Linkage Mechanism ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

A nonlinear optimization method is proposed to design a linkage mechanism used for opening and shutting a ship’s hatch cover. Considering the maximum force of the oil cylinder necessary to move the hatch cover as the objective function to be minimized, the design problem to determine the optimal configuration of linkage mechanism is formulated as a nonlinear optimization problem of minimax type. It it shown that the optimal solution can be derived by adopting the generalized reduced gradient algorithm together with a linkage statical simulation model, and the effectiveness of the algorithm is ascertained through a numerical study.

Nonlinear Optimization Using Generalized Hopfield Networks

1989 ◽  
Vol 1 (4) ◽  
pp. 511-521 ◽  
Author(s):  
Athanasios G. Tsirukis ◽  
Gintaras V. Reklaitis ◽  
Manoel F. Tenorio
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Hopfield Network ◽  
Systems Of Nonlinear Equations ◽  
Hopfield Networks ◽  
Dynamic View ◽  
Study Results ◽  
Content Addressable Memories ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

A nonlinear neural framework, called the generalized Hopfield network (GHN), is proposed, which is able to solve in a parallel distributed manner systems of nonlinear equations. The method is applied to the general nonlinear optimization problem. We demonstrate GHNs implementing the three most important optimization algorithms, namely the augmented Lagrangian, generalized reduced gradient, and successive quadratic programming methods. The study results in a dynamic view of the optimization problem and offers a straightforward model for the parallelization of the optimization computations, thus significantly extending the practical limits of problems that can be formulated as an optimization problem and that can gain from the introduction of nonlinearities in their structure (e.g., pattern recognition, supervised learning, and design of content-addressable memories).

A New Method to Solve the Kinematic Problems of Parallel Robots Using Generalized Reduced Gradient Algorithm

2016 ◽  
Vol 28 (3) ◽  
pp. 404-417 ◽  
Author(s):  
Thanh Trung Trang ◽  
◽  
Wei Guang Li ◽  
Thanh Long Pham ◽  
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
New Method ◽  
Gradient Algorithm ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Algorithm

[abstFig src='/00280003/17.jpg' width=""300"" text='Stewart Gough robot and the equivalent substitutional configuration' ] This paper proposes a new method of solving the kinematic problems for parallel robots. The paper content aims to solve nonlinear optimization problems with constraints rather than to directly solve high-order nonlinear systems of equations. The nonlinear optimization problems shall be efficiently solved by applying the Generalized Reduced Gradient algorithm and appropriate downgrade techniques. This new method can be able to find exact kinematic solutions by assigning constraints onto the parameters. The procedure can be done without filtering control results from mathematical solution, from which the control time of manipulators can be reduced. The numerical simulation results in this paper shall prove that the method can be applied to solve kinematic problems for a variety of parallel robots regardless of its structures and degree of freedom (DOF). There are several advantages of the proposed method including its simplicity leading to a shorter computing time as well as achieving high accuracy, high reliability, and quick convergence in final results. Hence, the applicability of this method in solving kinematic problems for parallel manipulators is remarkably high.

Optimization of a Novel Combined Power/Refrigeration Thermodynamic Cycle

Solar Energy ◽  
2002 ◽  
Author(s):  
Shaoguang Lu ◽  
D. Yogi Goswami
Keyword(s):  
Waste Heat ◽  
Thermodynamic Cycle ◽  
Cycle Performance ◽  
Working Fluid ◽  
Second Law ◽  
Optimum Conditions ◽  
Ambient Temperatures ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Performance Conditions

A novel combined power/refrigeration thermodynamic cycle is optimized for thermal performance in this paper. The cycle uses ammonia-water binary mixture as a working fluid and can be driven by various heat sources, such as solar, geothermal and low temperature waste heat. It could produce power as well as refrigeration with power output as a primary goal. The optimization program, which is based on the Generalized Reduced Gradient (GRG) algorithm, can be used to optimize for different objective functions. Examples that maximize second law efficiency, work output and refrigeration output are presented, showing the cycle may be optimized for any desired performance parameter. In addition, cycle performance over a range of ambient temperatures was investigated. It was found that for a source temperature of 360K, which is in the range of flat plate solar collectors, both power and refrigeration outputs are achieved under optimum conditions. All performance parameters, including first and second law efficiencies, power and refrigeration output decrease as the ambient temperature goes up. On the other hand, for a source of 440K, optimum conditions do not provide any refrigeration. However, refrigeration can be obtained even for this temperature under non-optimum performance conditions.

scholarly journals Optimasi Pemanfaatan Air Embung Kasih untuk Domestik dan Irigasi Tetes

2019 ◽  
Vol 13 (1) ◽  
pp. 41
Author(s):  
Segel Ginting ◽  
Dadan Rahmandani ◽  
Abid Hendri Indarta
Keyword(s):  
Reduced Gradient ◽  
Generalized Reduced Gradient

Pemerintah membangun Embung Kasih untuk mengatasi terbatasnya sumber air di Desa Tuatuka, Provinsi NTT. Embung tersebut digunakan untuk memenuhi kebutuhan domestik dan irigasi. Pengoperasian embung perlu direncanakan karena volume tampungan terbatas. Optimasi penggunaan air embung diperlukan untuk menentukan jumlah penggunaan air dengan berbagai skenario kondisi hujan. Simulasi penggunaan air tahun 1974 s.d. 2015 dilakukan sebagai evaluasi untuk menilai keberhasilan operasi embung. Penelitian ini dilakukan dengan tujuan untuk menentukan jumlah pemakaian air untuk kebutuhan domestik dan atau irigasi secara optimal. Optimasi dilakukan dengan Metode Generalized Reduced Gradient (GRG) untuk fungsi tujuan memaksimalkan penggunaan air embung. Hasil optimasi diperoleh dengan beberapa skenario. Skenario pertama untuk hujan normal, pemanfaatan air untuk domestik sekitar 2.604 orang atau untuk mengairi lahan seluas 2,746 ha dengan irigasi tetes. Skenario kedua untuk kondisi hujan ekstrim basah, pemanfaatan air untuk domestik sekitar 3.601 orang atau untuk irigasi tetes sekitar 4,698 ha. Skenario ketiga untuk kondisi hujan ekstrim kering, pemanfaatan air untuk domestik sekitar 454 orang atau untuk irigasi tetes sekitar 0,45 ha. Berdasarkan evaluasi hasil optimasi dengan menggunakan simulasi data tahun 1974 s.d. 2015, maka ditetapkan jumlah penggunaan air embung untuk domestik sekitar 454 orang dan irigasi tetes seluas 1 Ha dengan tingkat keandalan operasi embung mencapai 78,57%.

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