scholarly journals Program Linier Parametrik

2019 ◽  
Vol 2 (1) ◽  
pp. 69-76
Author(s):  
Adolf T Simatupang
Keyword(s):  
Objective Function ◽  
Optimal Solution ◽  
Critical Value ◽  
Critical Values ◽  
Linear Program ◽  
Linear Programs ◽  
Program Problem ◽  
Matrix Version ◽  
Linear Program Problem ◽  
The Matrix

This study aims to discuss a linear program problem where its constants can change, If a constant for a linear program problem is changed, then we don't need to count from the beginning again. Next, we will examine the properties of the objective function as a result of changes in these constants. In this discussion determine the non-negative "critical value" which provides the optimal solution to the problem of parametric linear programs. Searching for critical values in parametric linear programs is done by the matrix version method.

scholarly journals A New Algorithm for Privacy-Preserving Horizontally Partitioned Linear Programs

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Chengxue Zhang ◽  
Debin Kong ◽  
Peng Pan ◽  
Mingyuan Zhou
Keyword(s):  
Linear Programming ◽  
Random Matrix ◽  
Optimal Solution ◽  
Full Rank ◽  
Linear Programs ◽  
Program Problem ◽  
Constraint Matrix ◽  
Right Hand ◽  
Linear Program Problem ◽  
The Matrix

In a linear programming for horizontally partitioned data, the equality constraint matrix is divided into groups of rows. Each group of the matrix rows and the corresponding right-hand side vector are owned by different entities, and these entities are reluctant to disclose their own groups of rows or right-hand side vectors. To calculate the optimal solution for the linear programming in this case, Mangasarian used a random matrix of full rank with probability 1, but an event with probability 1 is not a certain event, so a random matrix of full rank with probability 1 does not certainly happen. In this way, the solution of the original linear programming is not equal to the solution of the secure linear programming. We used an invertible random matrix for this shortcoming. The invertible random matrix converted the original linear programming problem to a secure linear program problem. This secure linear programming will not reveal any of the privately held data.

scholarly journals Linear programming with inequality constraints via entropic perturbation

1996 ◽  
Vol 19 (1) ◽  
pp. 177-184 ◽  
Author(s):  
H.-S. Jacob Tsao ◽  
Shu-Cherng Fang
Keyword(s):  
Linear Inequality ◽  
Optimal Solution ◽  
Path Following ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Linear Program ◽  
Programming Approach ◽  
Linear Programs ◽  
Dual Program

A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. Anϵ-optimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Since cross-entropy minimization subject to linear inequality constraints is a special case of the perturbed linear program, the duality result becomes readily applicable. Many standard constrained optimization techniques can be specialized to solve the dual program. Such specializations, made possible by the simplicity of the constraints, significantly reduce the computational effort usually incurred by these methods. Immediate applications of the theory developed include an entropic path-following approach to solving linear semi-infinite programs with an infinite number of inequality constraints and the widely used entropy optimization models with linear inequality and/or equality constraints.

scholarly journals Exploring Students Computational Thinking based on Self-Regulated Learning in the Solution of Linear Program Problem

2019 ◽  
Vol 8 (1) ◽  
pp. 30
Author(s):  
Diah Nuraisa ◽  
Amalina Nur Azizah ◽  
Dian Nopitasari ◽  
Swasti Maharani
Keyword(s):  
Pattern Recognition ◽  
Problem Solving ◽  
Computational Thinking ◽  
Linear Program ◽  
Program Problem ◽  
Self Regulated Learning ◽  
Linear Program Problem ◽  
Regulated Learning ◽  
Depth Interviews

This study aims to analyze the students computational thinking in the solution of the linear program problem based on self-regulated learning. The data were collected by self-regulated learning questionnaire, computational thinking test, and depth interviews. This study was conducted in SMAN 10 Tangerang. Computational thinking in students with high and medium levels of self-regulated learning has no difference. Students still make a solution that is fixated with linear program problem-solving procedures in general, that is using examples, substitution, and elimination. In solving problems, students can reach the stages of decomposition and pattern recognition only. Students still do not evaluate the results of their work. Algorithmic performed is less coherent because the abstraction has not been done. The recommendation for further research is the need for research that can develop student abstraction in solving problems. Besides, there is also a need for research that analyzes the reflective of students in computational thinking when solving problems.

scholarly journals Profil Kemampuan Mahasiswa Tadris Matematika dalam Memecahkan Masalah Program Linear Ditinjau dari Perbedaan Tingkat Kemampuan Prasyarat dan Gaya Kognitif Fiel Dependent

2018 ◽  
Vol 6 (1) ◽  
pp. 29-46
Author(s):  
Sitti Zuhaerah Thalhah
Keyword(s):  
Problem Solving ◽  
Cognitive Style ◽  
Linear Program ◽  
Research Subjects ◽  
Program Problem ◽  
Good Ability ◽  
Linear Program Problem ◽  
Field Dependent ◽  
Ability Tests ◽  
Simplex Methods

Abstract:This research has been carried out on Semester II students of Mathematics education Department, Faculty of Tarbiyah and Teacher Training at IAIN Palopo in 2017. The type of this research is qualitative descriptive. This research aims to describe the ability of students in solving Linear Program problems in terms of differences in the level of prerequisite ability and cognitive style. The instruments were (1) GEFT test, (2) Linear Algebra prerequisite ability tests, (3) Linear Program problem solving tests, (4) and unstructured task-based interviews. The results of this study are (1) research subjects with high prerequisite ability dependent field cognitive style, showing good ability in understanding problems correctly, planning solutions, solving problems in accordance with the plan and re-examining the results obtained. Subjects can solve Linear Program problems with graph and simplex methods (2) research subjects with prerequisite abilities while field dependent cognitive style, able to understand problems correctly, still unsure when carrying out solutions, but according to plan. Subjects can solve Linear Program problems with graphical methods and simplex methods, (3) research subjects with low prerequisite ability in field dependent cognitive style, lack of ability to understand problems, unable to carry out problem solving correctly, and unsure in explaining the completion steps taken.Abstrak: Penelitian ini dilaksanakan di IAIN Palopo Fakultas Tarbiyah dan Ilmu Pendidikan Tadris Matematika Semester III Tahun 2017. Jenis penelitian ini adalah deskriptif kualitatif. Yang bertujuan mendeskripsikan kemampuan mahasiswa dalam memecahkan masalah Program Linier ditinjau dari perbedaan tingkat kemampuan prasyarat dan gaya kognitif. Instrumen yang digunakan adalah (1) tes GEFT, (2) tes kemampuan prasyarat Aljabar Linier, (3) tes pemecahan masalah Program Linier, (4) dan wawancara berbasis tugas tidak terstruktur. Hasil penelitian ini adalah (1) subjek penelitian dengan kemampuan prasyarat tinggi gaya kognitif field dependen, menunjukkan kemampuan yang baik dalam memahami masalah dengan tepat, merencanakan pemecahan, menyelesaikan masalah sesuai dengan rencana dan memeriksa kembali hasil yang diperoleh. Subjek dapat menyelesaikan masalah Program Linier dengan metode grafik dan simpleks (2) subjek penelitian dengan kemampuan prasyarat sedang gaya kognitif field dependent, dapat memahami masalah dengan tepat, masih kurang yakin saat melaksanakan pemecahan, namun sesuai dengan rencana. Subjek dapat menyelesaikan masalah Program Linier dengan metode grafik dan metode simpleks, (3) subjek penelitian dengan kemampuan prasyarat rendah gaya kognitif field dependent, kurang mampu memahami permasalahan, tidak mampu melaksanakan pemecahan masalah dengan benar, dan tidak yakin dalam menjelaskan langkah-langkah penyelesaian yang ditempuh.

scholarly journals Improving ADMMs for solving doubly nonnegative programs through dual factorization

4OR ◽  
2020 ◽  
Author(s):  
Martina Cerulli ◽  
Marianna De Santis ◽  
Elisabeth Gaar ◽  
Angelika Wiegele
Keyword(s):  
Objective Function ◽  
Large Scale ◽  
Objective Function Value ◽  
Optimal Solution ◽  
Stable Set ◽  
Dual Variable ◽  
Post Processing ◽  
Semidefinite Programs ◽  
The Matrix ◽  
The Impact

Abstract Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN), which are semidefinite programs where the elements of the matrix variable are constrained to be nonnegative. Starting from two algorithms already proposed in the literature on conic programming, we introduce two new ADMMs by employing a factorization of the dual variable. It is well known that first order methods are not suitable to compute high precision optimal solutions, however an optimal solution of moderate precision often suffices to get high quality lower bounds on the primal optimal objective function value. We present methods to obtain such bounds by either perturbing the dual objective function value or by constructing a dual feasible solution from a dual approximate optimal solution. Both procedures can be used as a post-processing phase in our ADMMs. Numerical results for DNNs that are relaxations of the stable set problem are presented. They show the impact of using the factorization of the dual variable in order to improve the progress towards the optimal solution within an iteration of the ADMM. This decreases the number of iterations as well as the CPU time to solve the DNN to a given precision. The experiments also demonstrate that within a computationally cheap post-processing, we can compute bounds that are close to the optimal value even if the DNN was solved to moderate precision only. This makes ADMMs applicable also within a branch-and-bound algorithm.

Effect of temperature on matrix multicracking evolution of C/SiC fiber-reinforced ceramic-matrix composites

2020 ◽  
Vol 39 (1) ◽  
pp. 189-199
Author(s):  
Longbiao Li
Keyword(s):  
Strain Energy ◽  
Ceramic Matrix Composites ◽  
Critical Value ◽  
Matrix Cracking ◽  
Interface Debonding ◽  
Matrix Composites ◽  
Temperature Dependent ◽  
Damage State ◽  
The Matrix ◽  
Sic Composites

AbstractIn this paper, the temperature-dependent matrix multicracking evolution of carbon-fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) is investigated. The temperature-dependent composite microstress field is obtained by combining the shear-lag model and temperature-dependent material properties and damage models. The critical matrix strain energy criterion assumes that the strain energy in the matrix has a critical value. With increasing applied stress, when the matrix strain energy is higher than the critical value, more matrix cracks and interface debonding occur to dissipate the additional energy. Based on the composite damage state, the temperature-dependent matrix strain energy and its critical value are obtained. The relationships among applied stress, matrix cracking state, interface damage state, and environmental temperature are established. The effects of interfacial properties, material properties, and environmental temperature on temperature-dependent matrix multiple fracture evolution of C/SiC composites are analyzed. The experimental evolution of matrix multiple fracture and fraction of the interface debonding of C/SiC composites at elevated temperatures are predicted. When the interface shear stress increases, the debonding resistance at the interface increases, leading to the decrease of the debonding fraction at the interface, and the stress transfer capacity between the fiber and the matrix increases, leading to the higher first matrix cracking stress, saturation matrix cracking stress, and saturation matrix cracking density.

scholarly journals Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dipankar Barman ◽  
Subhajit Barman ◽  
Bibhas Ranjan Majhi
Keyword(s):  
Mutual Information ◽  
Critical Point ◽  
Thermal Field ◽  
Narrow Range ◽  
Critical Value ◽  
Critical Values ◽  
Parallel Motion ◽  
Field Temperature ◽  
The Right

Abstract We investigate the effects of field temperature T(f) on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, T(f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively. While for T(f) = 0 entanglement harvesting is possible for all values of A’s acceleration aA, in the presence of temperature, it is possible only within a narrow range of aA. In (1 + 1) dimensions, the range starts from specific values and extends to infinity, and as we increase T(f), the minimum required value of aA for entanglement harvesting increases. Moreover, above a critical value aA = ac harvesting increases as we increase T(f), which is just opposite to the accelerations below it. There are several critical values in (1 + 3) dimensions when they are in different accelerations. Contrary to the single range in (1 + 1) dimensions, here harvesting is possible within several discrete ranges of aA. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to (1 + 1) dimensional results. We also discuss the dependence of mutual information among these detectors on aA and T(f).

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