Let S be a nonempty, closed, convex set in a Euclidean space X and y a point
Question:
1. There exists a point x0 e S which is closest to y, that is,
||x0 - y|| ≤ ||x - y|| for every x ∊ S
2. x0 is unique
3. (x0 - y)T(x - x0) ≥ 0 for every x ∊ S
Finite dimensionality is not essential to the preceding result, although completeness is required.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 77% (9 reviews)
1 Choose some and let be the set of all x which are closer to y than that is x x y x y is compact ...View the full answer
Answered By
Sarfraz gull
have strong entrepreneurial and analytical skills which ensure quality tutoring and mentoring in your international business and management disciplines. Over last 3 years, I have expertise in the areas of Financial Planning, Business Management, Accounting, Finance, Corporate Finance, International Business, Human Resource Management, Entrepreneurship, Marketing, E-commerce, Social Media Marketing, and Supply Chain Management.
Over the years, I have been working as a business tutor and mentor for more than 3 years. Apart from tutoring online I have rich experience of working in multinational. I have worked on business management to project management.
5.00+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Numerical Analysis questions
-
Let S be a nonempty compact convex subset of a normed linear space X. 1. Let
-
Let S be a nonempty set in a normed linear space X. Show 1. S* is a closed convex cone in X* 2. S** is a closed convex cone in X 3. S S**
-
Let S be a nonempty bounded set in R. (a) Let a > 0, and let aS := {as : s S}. Prove that Inf(aS) = a inf S; sup(aS) = a sup S: (b) Let b < 0 and let bS = {bs : s S}. Prove that Inf(bS) = b sup S;...
-
Find the total heat loss from a room in units (1 unit = 1 kWh); the U-values and surface areas of the different elements are given in the Table 1. The inside and outside air temperatures are 10 C and...
-
Complete the following two-way ANOVA table. Determine the critical table F values and reach conclusions about the hypotheses for effects. Let =.05. df Source of Variance Row Column Interaction Error...
-
Determine the equivalent circuit for the line in Problem 5.26. Problem 5.26 A 350 k m , 500 k V , 60 H z 350 k m , 500 k V , 60 H z , three-phase uncompensated line has a positivesequence...
-
Explain the purpose of the temperature variable in simulated annealing. How effective would the method be without it?
-
Woolrich Companys market research division has projected a substantial increase in demand over the next several years for one of the companys products. To meet this demand, the company will need to...
-
During 2020, The Chen Corporation had the following actual results: Finished Units: Units Completed and Sold Thing One 65,000 Thing Two 40,000 (Assume the sales price per unit was the same as the...
-
1. Construct truth tables for the following PC wff and use the tables to determine whether or not each is PC-valid: (a) p (b) ~ (p q) (~ p ~ q) (c) ~ (p (q ~ p)) r 2. Explain with reference to...
-
If x y, then ||x + y||2 = ||x||2 + ||y||2 The next result provides the crucial step in establishing the separating hyperplane theorem (section 3.9).
-
Generalize the preceding exercise to any Hilbert space. Specifically, let S be a nonempty, closed, convex set in Hilbert space X and y B S. Let Then there exists a sequence (xn) in S such that || xn...
-
The hospital period, in days, for patients following treatment for a certain type of kidney disorder is a random variable Y = X + 4, where X has the density function(a) Find the probability density...
-
Suppose a transistor consists of a very narrow \(p\)-type material sandwiched between two very wide regions of \(n\)-type material. (a) Is the charge on the \(p\)-type region positive or negative,...
-
A \(6.00-\mathrm{mH}\) solenoid is connected in series with a \(1.0-\mu \mathrm{F}\) capacitor and an AC source. The solenoid has internal resistance \(3.0 \Omega\), which can be treated as a series...
-
How might governments around the world collaborate to support green and sustainable finance?
-
(a) If each vertical gray line in Figure \(32.4 b\) represents \(0.020 \mathrm{~s}\), what is the frequency of the oscillation? (b) What is the average potential difference across the capacitor in...
-
What national policies could governments introduce to support green and sustainable finance?
-
Define PPE and explain how materiality affects the concept of PPE.
-
Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. What was the annual growth rate?
-
Use the gasoline mileage data in Exercise 12-5 to build regression models using the following techniques: (a) All possible regressions. Find the minimum Cp and minimum MSE equations. (b) Stepwise...
-
Consider the electric power data in Exercise 12-6 Build regression models for the data using the following techniques? (a) All possible regressions. (b) Stepwise regression. (c) Forward selection....
-
Consider the wire bond pull strength data in Exercise 12-8. Build regression models for the data using the following methods: (a) Stepwise regression. (b) Forward selection. (c) Backward elimination....
-
You will make a post giving your point-of-view (PoV) on a brand's activities and/or marketing campaign. Give your PoV on what brands can and should do to ensure they are creating a great digital...
-
IM.83 A distribution center for a sporting goods retailer places orders with manufacturers for a variety of items. Among these is a popular standard skateboard, targeted to first-time skate boarders....
-
[5] 5. Determine the area of the shaded region, if the radius of each circle is 5 cm.
Study smarter with the SolutionInn App