For concavity and convexity is that the Hessian be negative semidefinite and positive semidefinite But for strict concavity definiteness is only the sufficient condition not the necessary . What is the necessary condition for a two variable function to ensure strict concavity / convexity ?
2026-04-07 21:22:06.1775596926
What are the Necessary and sufficient conditions for concavity and convexity of a two variable function?
2.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in OPTIMIZATION
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- optimization with strict inequality of variables
- Gradient of Cost Function To Find Matrix Factorization
- Calculation of distance of a point from a curve
- Find all local maxima and minima of $x^2+y^2$ subject to the constraint $x^2+2y=6$. Does $x^2+y^2$ have a global max/min on the same constraint?
- What does it mean to dualize a constraint in the context of Lagrangian relaxation?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Building the model for a Linear Programming Problem
- Maximize the function
- Transform LMI problem into different SDP form
Related Questions in CONVEX-ANALYSIS
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
- Convex open sets of $\Bbb R^m$: are they MORE than connected by polygonal paths parallel to the axis?
- Show that this function is concave?
- In resticted domain , Applying the Cauchy-Schwarz's inequality
- Area covered by convex polygon centered at vertices of the unit square
- How does positive (semi)definiteness help with showing convexity of quadratic forms?
- Why does one of the following constraints define a convex set while another defines a non-convex set?
- Concave function - proof
- Sufficient condition for strict minimality in infinite-dimensional spaces
- compact convex sets
Related Questions in CONVEX-OPTIMIZATION
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- Least Absolute Deviation (LAD) Line Fitting / Regression
- Check if $\phi$ is convex
- Transform LMI problem into different SDP form
- Can a linear matrix inequality constraint transform to second-order cone constraint(s)?
- Optimality conditions - necessary vs sufficient
- Minimization of a convex quadratic form
- Prove that the objective function of K-means is non convex
- How to solve a linear program without any given data?
- Distance between a point $x \in \mathbb R^2$ and $x_1^2+x_2^2 \le 4$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Your initial statement is wrong: the Hessian does not have to exist for the function to be concave or convex. For example, $|x|$ is convex but does not have derivatives at $0$.
A necessary and sufficient condition for a convex/concave function to be strictly convex/concave is that its graph does not contain any line segment.