Question: Let S be convex set in n which contains no interior points of the nonnegative orthant n+. Then there exists a hyperplane with nonnegative normal

Let S be convex set in ℜn which contains no interior points of the nonnegative orthant ℜn+. Then there exists a hyperplane with nonnegative normal p ≩ 0 (that is p ≠ 0, pi ≥ 0) such that pTx ≤ 0 for every x ∈ S.

Step by Step Solution

★★★★★

3.57 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let denote the positive orthant of is a convex set indeed cone with a nonempty ... 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 (561).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Let S be convex set in n that contains no interior points of the non positive orthant n-. Then there exists a hyperplane with nonnegative normal p 0 such that pTx 0 for every x S

Suppose that x* = (x*1, x*2,..., x*n) is a Pareto efficient allocation in an exchange economy with l commodities and n consumers (example 1.117). Assume that ¢ Individual preferences are convex,...

Let S be a nonempty convex set in n with 0 S. 1. For every point a S, define the polar set S*a = {x n : ||x|| = 1; xTa ¥ 0}. S*a is a nonempty closed set. 2. For any finite set of points {a1, a2,...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Let K be a closed convex cone that intersects the nonnegative orthant at 0, that is, K n+ = {0}. Then there exists a hyperplane with positive normal p > 0 (i.e., pi > 0 for every i) such that pTx 0...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Numerous exchange rate forecasting services exist. Tridents CFO Maria Gonzalez is considering whether to subscribe to one of these services at a cost of $20,000 per year. The price includes online...

The row echelon form of an augmented matrix of a linear system with 4 equations in the 4 [1 2 3 4 5] 0 0 1 2 0 0 0 0 0 0 Lo o o 0 unknowns is The free variables of the system are

Is it necessary to test each coefficient individually to see if either earnings per share or stock price is related to dividend yield? Why or why not?

A project is seriously delayed. Earned value analysis shows that the project needs to be completed ten percent faster than the work has been going. To get the project back on track, management wants...

Feller5 discusses the statistics of flying bomb hits in an area in the south of London during the Second World War. The area in question was divided into 24 24 = 576 small areas. The total number of...

The kings coinmaster boxes his coins 500 to a box and puts 1 counterfeit coin in each box. The king is suspicious, but, instead of testing all the coins in 1 box, he tests 1 coin chosen at random out...

In one of the first studies of the Poisson distribution, von Bortkiewicz7 considered the frequency of deaths from kicks in the Prussian army corps. From the study of 14 corps over a 20-year period,...

According to 7News, pet adoptions recorded a spike during the COVID 19 lockdown period. A veterinary clinic owner wanted to know the proportion of people who adopted a pet during the same period in...

Suppose you write 24 call option contracts with a $70 strike. The premium is $2.89. Evaluate your potential gains and losses at option expiration for stock prices of $60, $70, and $80. (Input all...

Two customers enter a store. Independently, they make decisions to purchase or not to purchase.The following diagrams shows how the outcomes can occur and combine with red bolding of sequence...