A differentiable function f: S R is pseudoconvex if f(x) < f(x0) f(x0)T(x - x0)

Question:

A differentiable function f: S → R is pseudoconvex if
f(x) < f(x0) ⇒ ∇f(x0)T(x - x0) < 0 for every x, x0 in S

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:52 AM

See More Questions

A differentiable function f : I R is said to be uniformly differentiable on I := (a, b) if for every Îµ > 0 there exists Î´ > 0 such that if 0 Show that if f is uniformly...
Let fn (x) := xn/n for x [0, 1]. Show that the sequence (fn) of differentiable functions converges uniformly to a differentiable function f on [0, 1], and that the sequence (fn) converges on [0, 1]...
Show that the gradient of a differentiable function f points in the direction of greatest increase.
Alpha Corp. (a spinoff of Alpha Beta) makes Product X, which is composed of two Part Ys. Complete the following MRP matrices for X and Y, and construct a planned order report. When are orders placed...
Because of uncertainty in real estate markets, many homeowners are considering remodeling and constructing additions rather than selling. Probably the most expensive room in the house to remodel is...
Critical Thinking Age segmentation is a generally common approach for small businesses in particular, as it is a simple and easy method of segmentation. Considering your own peer group (which is...
What selection criteria does Trek utilize when it selects a new supplier or evaluates an existing supplier?
What is the specific purpose of an acceptable use policy?
Chromatic Polynomial of Disconnected Graphs (a) (2 points) Prove that the chromatic polynomial of a disjoint graph is the the product of the polynomials of components. (b) (3 points) If G has r...
Consider the E-R diagram in Figure 7.29, which models an online bookstore. a. List the entity sets and their primary keys. b. Suppose the bookstore adds Blu-ray discs and downloadable video to its...
Suppose that a differentiable functional f on an open set S n is quasiconcave. At every regular point f(x0) 0, A restricted form of quasiconcavity is useful in optimization (see section 5.4.3). A...
Show that 1. Every differentiable concave function is pseudoconcave. 2. Every pseudoconcave function is quasiconcave
What is the Phillips curve? Does the Phillips curve relationship hold for U.S. data? Explain.
If Technical Specification 2 were reduced in the next design for this product, what would likely happen to customer opinion of Value Feature A? Quick Start QFD Matrix 2 Strong positive correlation...
Customer opinion of Value Feature B is most strongly correlated with what technical specification? Quick Start QFD Matrix 2 Strong positive correlation Some positive correlation == Strong negative...
Consider Quick Start QFD Matrix 1 above. Of the two value features, which do cus- tomers consider three times more important? Quick Start Quick Start QFD Matrix 1 = Strong positive correlation = Some...
Which technical spec can be most easily modified without changing current choices for the other two technical specs? Quick Start Quick Start QFD Matrix 1 = Strong positive correlation = Some positive...
Use Table A.1 to select 20 three-digit random numbers. Did any of the numbers occur more than once? How is it possible for a number to occur more than once? Make a stem-and-leaf plot of the numbers...
What are some of the ways that TAMLs are used?
Beginning with a country that has a trade deficit, demonstrate graphically what will happen to a countrys potential output with globalization if that countrys costs of production fall. Explain your...
Sketch the graph of the function g (x) = | x2 4 | | x2 4 |.
Draw the graph of the equation x + |x| = y + | y |.
Draw the graph of the equation x4 4x2 x2y2 + 4y2 = 0.
Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all - equity firm that specializes in this business. Suppose Harburtin ' s equity beta is 0 . 8 7 , the...
Ned Allen opened a medical practice in Los Angeles, California, and had the following transactions during the month of January. (Click the icon to view the January transactions.) Journalize the...
do you need more information or are you working on this? Irene Watts and John Lyon are forming a partnership to which Watts will devote one- half time and Lyon will devote full time. They have...

A differentiable function f: S R is pseudoconvex if f(x) < f(x0) f(x0)T(x - x0)

Question:

Step by Step Answer:

Suppose x x 0 x 0 x x ...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions