Question: If is a weak order on X, x y (x) (y) x y (x) (y) The principal task

If ≿ is a weak order on X,
x ≿ y ⇒ ≿(x) ⊂ ≿(y)
x ≻ y ⇒ ≻(x) ⊂ ≻(y)
The principal task of optimization theory and practice is identify the best element(s) in a choice set X, which is usually weakly ordered by some criterion. To identify the best element, optimization theory draws on other properties (linear and metric) of the choice set. Techniques of optimization are explored in chapter 5. To prepare the ground, we next investigate the metric and linear properties of sets in sections 1.3 and 1.4. Before leaving order relations, we touch on the problem of aggregating different orders on a common set.

Step by Step Solution

★★★★★

3.43 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Assume and Then by transitivity Therefore This ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (258).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

If is a weak order on X, then for every y X, 1. (y) (y) = X and (y) (y) = Iy 2. (y) (y) = X and (y) (y) = 3. (y), Iy and (y) together partition X

Is the deficit order d defined in example 1.49 A partial order? A weak order? on the set X.

You are the vice president of a consumer electronics company that needs to determine whether or not to introduce a new product to the market. Either your company can manufacture it or you can...

help me please question 1 Time Value of Money - A key financial principle stating that a dollar today is worth more than a dollar tomorrow. The present value of money is the value today of a cash...

5 Attraction to Groups Learning Objectives What We Will Be Investigating What makes a group work most efficiently? What techniques are available to make group members feel more as if they are part of...

N A S TIO I C VE A N T I IZ O E T N R C A TI O PE G CA E S R NI H R T E O U P OR M 2 F OM E R T P C A L C H A L LEARNING OBJECTIVES After studying this chapter, you will be able to answer several...

Solving Two-stage Robust Optimization Problems by A Constraint-and-Column Generation Method Bo Zeng Department of Industrial and Management Systems Engineering University of South Florida, Email:...

MGT 3090 Prof. Si Ahn Mehng Conflict Styles Inventory Instructions: The Conflict Styles Inventory consists of eight common community conflict situations. After reading each situation, you will need...

Developments in Technology Light is incident from air on the end face of a multimode optical fibre at angle of incidence as shown below. n n 1 2 The refractive indices of the core and cladding are...

false, and justify 4. Determine whether or not each of the following statements is true or or a counterexample. proof your answer with a (a) (3 points) Jrz dz = dz, where T is the positively oriented...

import java.util.Scanner; /* * This program counts the number of vowels in a sentence where the string * * For example, if the sentence string is "hello how are you" the number of vowels is: * * 7...

2. What specific actions have you and your co-managers taken to develop core competencies or competitive capabilities that can contribute to good strategy execution and potential competitive...

You have a number of costs to track and manage because your project is technically very complex. They include direct costs and indirect (overhead) costs. You have found that managing overhead costs...

The random variable is the number of nonconforming solder connections on a printed circuit board with 1000 connections.

In a voice communication system with 50 lines, the random variable is the number of lines in use at a particular time.

An electronic scale that displays weights to the nearest pound is used to weigh packages. The display shows only five digits. Any weight greater than the display can indicate is shown as 99999. The...

Consider the following data for Nike Inc, in 2009 it had 19,250 million in sales with a 10% growth rate in 2010, but then slows by 1% to the long-run growth rate of 5% by 2015. Nike expects EBIT to...

use powerquery to access database

In English: Analyze in a minimum of two sentences the results obtained in the Cash Budget. Question: Discuss the purpose of a financial manager who devotes so much of his time and energy to the...