Optimality conditions and sensitivity analysis of cone-constrained and semi-definite programs

1998 ◽  
pp. 1-15
Author(s):  
Alexander Shapiro
Keyword(s):  
Sensitivity Analysis ◽  
Optimality Conditions

scholarly journals ALGORITHM FOR CONTROLLING THE SPECTRUM OF EIGENFREQUENCIES AND VIBRATION MODES BY CHARDING THE GEOMETRIC PARAMETERS OF MAST SESTEMS

2021 ◽  
pp. 6-18
Author(s):  
Vladimir Grinyov ◽  
Vitaliy Vynogradov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Maximum Principle ◽  
Optimality Conditions ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Maximum Principle ◽  
Natural Frequency Spectrum

The article considers a model of a mast with six levels of fastening of cables. The main attention in the work is considered to the methods of control of the natural frequency spectrum, due to the use of methods of sensitivity analysis and optimization. The above task is achieved by varying the cross-sectional area of the pipes - racks. Automation of computational processes is provided by programming the built-in module in the Revit program. For more convenient and faster control of the natural frequency spectrum, the algorithm described above was written in a free add-on for Revit - Dynamo. With the help of so-called nodes, an application was created that took data from the depicted 3D model Revit and performed calculations. This allows you to easily use optimality conditions similar to the maximum principle. The sensitivity analysis for the first and second own is carried out in the work. The mechanism of their management within the limits of the investigated model is shown. The relations in the case of the problem of finding the natural frequency extremum with a given number are given, provided that the total amount of varied bands is fixed. The numerical control algorithm is based on the necessary optimality conditions in the form of the maximum principle for rod models. A variant of varying the area of the belts along the height of the mast is proposed. The sensitivity analysis for the first and second natural frequencies is carried out and its use for construction of effective computational process is shown. Based on the results of the work, a working software algorithm was created for fast analysis of mast oscillations on extensions. Graphs of zones of possible change of the first and second frequencies are resulted. The distribution of the cross-sectional area for frequencies is shown. To compare the results of natural frequency calculations on other calculation models, the first and second natural frequencies of bending oscillations were calculated by the finite element method in the SCAD complex. The errors for the points of the curves (constant in the height of the mast area of the belts) do not exceed 10%. It should be noted that the consideration of optimization problems of the above type on the basis of finite element models is quite difficult; for them it is not possible to formulate the necessary conditions of optimality similar to the principle of maximum.

MLP in Layer-Wise Form with Applications to Weight Decay

2002 ◽  
Vol 14 (6) ◽  
pp. 1451-1480 ◽  
Author(s):  
Tommi Kärkkäinen
Keyword(s):  
Sensitivity Analysis ◽  
Optimality Conditions ◽  
Numerical Experiments ◽  
Local Optimality ◽  
Learning Problem ◽  
Weight Decay ◽  
Mlp Network ◽  
General Calculus

A simple and general calculus for the sensitivity analysis of a feedforward MLP network in a layer-wise form is presented. Based on the local optimality conditions, some consequences for the least-means-squares learning problem are stated and further discussed. Numerical experiments with formulation and comparison of different weight decay techniques are included.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Aplikasi Metode Hungarian Dalam Optimalisasi Waktu Penugasan Karyawan dan Keuntungan Produksi Home Industry

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Empya Charlie ◽  
Siti Rusdiana ◽  
Rini Oktavia
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Optimal Scheduling ◽  
Total Work ◽  
Work Time ◽  
Hungarian Method ◽  
Total Work Time

Penelitian ini bertujuan untuk mengoptimalkan penjadwalan karyawan di CV. Karya Indah Bordir dalam melakukan tugas-tugas tertentu menggunakan metode Hungaria, serta menganalisis sensitivitas solusi optimal jika ada pengurangan waktu karyawan untuk menyelesaikan tugas-tugas. Metode Hongaria diterapkan pada proses bordir yang melibatkan 11 karyawan dan 10 tugas. Hasil penjadwalan yang optimal meminimalkan waktu produksi bordir perusahaan. Hasil penjadwalan optimal yang ditemukan adalah: karyawan 1 mengerjakan tas Mambo, karyawan 2 mengerjakan tas Elli, karyawan 3 mengerjakan tas Lonjong, karyawan 4 mengerjakan tas Tampang bunga, karyawan 6 mengerjakan tas Ransel, karyawan 7 mengerjakan tas Tima, karyawan 8 mengerjakan tas Keong, karyawan 9 mengerjakan tas Alexa, karyawan 10 mengerjakan tas Luna, dan karyawan 11 mengerjakan tas Mikha, dengan total waktu kerja adalah 13,7 jam. Setelah metode Hongaria diterapkan, CV. Karya Indah Bordir mendapat peningkatan pendapatan sebanyak 9,09%. Analisis sensitivitas dilakukan dengan mengurangi waktu karyawan dalam menyulam tas. Hasil analisis sensitivitas adalah beberapa batasan untuk variabel basis dan non basis untuk mempertahankan solusi optimal.   This research has a purpose to optimize the scheduling of employees in CV. Karya Indah Bordir in doing certain tasks using Hungarian method, as well as analyzing the sensitivity of the optimal solution if there is a reduction on the employees time to finish the tasks. The Hungarian method was applied on the embroidery process involving 11 employees and 10 tasks. The optimal scheduling result minimize the time of the embroidery production of the company. The optimal scheduling result found is: employee 1 does the Mambo bag, employee 2 does the Elli bag, employee 3 does the Lonjong bag, employee 4 does the Tampang bunga bag, employee 6 does the Ransel, employee 7 does the Tima bag, employee 8 does the Keong bag, employee 9 does the Alexa bag, employees 10 does the Luna bag, and employee 11 does the Mikha bag, with the total work time is 13,7 hours. After the Hungarian method was applied, CV. Karya Indah Bordir got the increasing revenue as much as 9,09 %. The sensitivity analysis was conducted by reducing the time of the employees take in embroidery the bags. The results of the sensitivity analysis are some boundaries for basis and non basis variables to maintain the optimal solution. 

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