Operations Research (3): Theory

5.0

estrellas

10 calificaciones

孔令傑 (Ling-Chieh Kung)

ofrecido por

Operations Research (3): Theory

Universidad Nacional de Taiwán

Acerca de este Curso

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Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Electrical Engineering, etc.
The series of courses consists of three parts, we focus on deterministic optimization techniques, which is a major part of the field of OR.
As the third part of the series, we study mathematical properties of linear programs, integer programs, and nonlinear programs. We also introduce applications of these theoretical properties: How they help us develop better ways to solve mathematical programs.

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Nivel avanzado

This course is appropriate for students with experience Calculus, Linear Algebra, and Probability.

Aprox. 14 horas para completar

Inglés (English)

Subtítulos: Inglés (English)

Qué aprenderás

Understand the theoretical properties of linear programs, integer programs, and nonlinear programs.

Apply the mathematical properties to reduce the complexity of real-world problems or to solve it.

Habilidades que obtendrás

TheoryBusiness AnalyticsMathematical Optimization

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.

Certificado para compartir

Obtén un certificado al finalizar

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.

Nivel avanzado

This course is appropriate for students with experience Calculus, Linear Algebra, and Probability.

Aprox. 14 horas para completar

Inglés (English)

Subtítulos: Inglés (English)

Instructor

孔令傑 (Ling-Chieh Kung)

副教授 (Associate Professor)

資訊管理學系 (Department of Information Management)

34.268 alumnos

8 cursos

ofrecido por

Universidad Nacional de Taiwán

We firmly believe that open access to learning is a powerful socioeconomic equalizer. NTU is especially delighted to join other world-class universities on Coursera and to offer quality university courses to the Chinese-speaking population. We hope to transform the rich rewards of learning from a limited commodity to an experience available to all.

Programa - Qué aprenderás en este curso

Semana

Semana 1

1 hora para completar

Course Overview

In the first lecture, after introducing the course and the importance of mathematical properties, we study the matrix way to run the simplex method. Being more familiar with matrices will help us understand further lectures.

1 hora para completar

5 videos (Total 65 minutos), 1 lectura, 1 cuestionario

Semana

Semana 2

2 horas para completar

Duality

In this week, we study the theory and applications of linear programming duality. We introduce the properties possessed by primal-dual pairs, including weak duality, strong duality, complementary slackness, and how to construct a dual optimal solution given a primal optimal one. We also introduce one important application of linear programming duality: Using shadow prices to determine the most critical constraint in a linear program.

2 horas para completar

14 videos (Total 120 minutos)

14 videos

2-0: Opening.4m

2-1: Introduction.1m

2-2: Primal-dual pairs – The first example.8m

2-3: Primal-dual pairs – More examples.7m

2-4: Primal-dual pairs – General rule.12m

2-5: Weak duality and sufficiency of optimality.7m

2-6: Dual optimal solution and strong duality.11m

2-7: An example for the theorems.5m

2-8: Complementary slackness.12m

2-9: Motivating examples for shadow prices.9m

2-10: Shadow prices.9m

2-11: Shadow prices and duality.12m

2-12: Computers – Gurobi and Python for shadow prices.13m

2-13: Closing remarks.4m

1 ejercicio de práctica

Quiz for Week 220m

Semana

Semana 3

1 hora para completar

Sensitivity Analysis and Dual Simplex Method

In the past two weeks, we study the simplex method and the duality. On top of them, the dual simplex method is discussed in this lecture. We apply it to one important issue in sensitivity analysis: evaluating a linear programming model with a new constraint. A linear programming model with a new variable is also discussed.

1 hora para completar

8 videos (Total 52 minutos)

Semana

Semana 4

2 horas para completar

Network Flow

In this lecture, we introduce network flow models, which are widely used for making decision regarding transportation, logistics, inventory, project management, etc. We first introduce the minimum cost network flow (MCNF) model and show hot it is the generalization of many famous models, including assignment, transportation, transshipment, maximum flow, and shortest path. We also prove a very special property of MCNF, total unimodularity, and how it connects linear programming and integer programming.

2 horas para completar

10 videos (Total 80 minutos)

Semana

Semana 5

2 horas para completar

Convex Analysis

As the last lesson of this course, we introduce a case of NEC Taiwan, which provides IT and network solutions including cloud computing, AI, IoT etc. Since maintaining all its service hubs is too costly, they plan to rearrange the locations of the hubs and reallocate the number of employees in each hub. An algorithm is included to solve the facility location problem faced by NEC Taiwan.

2 horas para completar

13 videos (Total 125 minutos)

13 videos

5-0: Opening.4m

5-1: Motivating examples.7m

5-2: Convex sets and functions.12m

5-3: Global optimality and extreme point.11m

5-4: Convex programming.13m

5-5: Convexity of twice differentiable functions.6m

5-6: Example – EOQ12m

5-7: Second-order derivatives.8m

5-8: Positive semi-definiteness.13m

5-9: Analytically solving multi-variate NLPs.6m

5-10: Example – Two-product pricing.10m

5-11: Computers – Implementation of gradient descent.13m

5-12: Closing remarks.3m

1 ejercicio de práctica

Quiz for Week 520m

Semana

Semana 6

2 horas para completar

Lagrangian Duality and the KKT condition

In this week, we study nonlinear programs with constraints. We introduce two major tools, Lagrangian relaxation and the KKT condition, for solving constrained nonlinear programs. We also see how linear programming duality is a special case of Lagrangian duality.

2 horas para completar

15 videos (Total 120 minutos)

15 videos

6-0: Opening.5m

6-1: Motivation.8m

6-2: Lagrange relaxation.7m

6-3: An example of Lagrange relaxation.4m

6-4: Weak duality of Lagrange relaxation.6m

6-5: The KKT condition.9m

6-6: Visualizing the KKT condition.11m

6-7: Example 1 of applying the KKT condition.10m

6-8: Example 2 of applying the KKT condition.14m

6-9: The KKT condition in general.4m

6-10: More about Lagrange duality.3m

6-11: Convexity and strong duality of Lagrange relaxation.9m

6-12: An example of Lagrange duality.9m

6-13: Lagrange duality vs. LP duality.10m

6-14: Closing remarks.4m

1 ejercicio de práctica

Quiz for Week 620m

Semana

Semana 7

2 horas para completar

Case Study

In this week, we introduce two well-known models constructed by applying the mathematical properties we have introduced. First, we formulate a simple linear regression problem as a nonlinear program and derive the closed-form regression formula. Second, we introduce support-vector machine, one of the most famous classification model, from the perspective of duality.

2 horas para completar

14 videos (Total 90 minutos)

14 videos

7-0: Opening.6m

7-1: Introduction.3m

7-2: Simple linear regression.6m

7-3: Solving the simple linear regression problem.8m

7-4: Remarks and other regression models.8m

7-5: Support vector machine.8m

7-6: Formulating the SVM model.9m

7-7: Simplifying the objective function.4m

7-8: SVM for imperfect separation.6m

7-9: Dualization for the SVM problem (1).7m

7-10: Dualization for the SVM problem (2).5m

7-11: Convexity of the dual program.5m

7-12: Final remarks.3m

7-13: Closing remarks.5m

1 ejercicio de práctica

Quiz for Week 720m

Semana

Semana 8

1 hora para completar

Course Summary and Future Learning Directions

In the final week, we review the topics we have introduced and give some concluding remarks. We also provide some learning directions for advanced studies.

1 hora para completar

3 videos (Total 29 minutos)

Preguntas Frecuentes

When will I have access to the lectures and assignments?
El acceso a las clases y las asignaciones depende del tipo de inscripción que tengas. Si tomas un curso en modo de oyente, verás la mayoría de los materiales del curso en forma gratuita. Para acceder a asignaciones calificadas y obtener un certificado, deberás comprar la experiencia de Certificado, ya sea durante o después de participar como oyente. Si no ves la opción de oyente:
es posible que el curso no ofrezca la opción de participar como oyente. En cambio, puedes intentar con una Prueba gratis o postularte para recibir ayuda económica.
Es posible que el curso ofrezca la opción 'Curso completo, sin certificado'. Esta opción te permite ver todos los materiales del curso, enviar las evaluaciones requeridas y obtener una calificación final. También significa que no podrás comprar una experiencia de Certificado.
¿Qué recibiré si compro el Certificado?
Cuando compras un Certificado, obtienes acceso a todos los materiales del curso, incluidas las tareas calificadas. Una vez que completes el curso, se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes participar del curso como oyente sin costo.
Is financial aid available?
Sí, Coursera ofrece ayuda económica a los estudiantes que no pueden pagar la tarifa. Solicítala haciendo clic en el vínculo de Ayuda económica que está debajo del botón 'Inscribirse' a la izquierda. Se te pedirá que completes una solicitud y recibirás una notificación cuando se apruebe. Obtén más información.

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Operations Research (3): Theory

Operations Research (3): Theory