Does $$\min_{x \in X} \sum_{t=1}^n f_t(x) \geq \sum_{t=1}^n\min_{x \in X} {f_t(x)}$$ hold?
This is a conclusion I want to use and I feel it's right but I can't prove.
Is it true?
Note: f is convex in X
2026-04-24 04:03:05.1777003385
Is the minimized sum greater than the sum of the minimum values?
262 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ANALYSIS
- Analytical solution of a nonlinear ordinary differential equation
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Show that $d:\mathbb{C}\times\mathbb{C}\rightarrow[0,\infty[$ is a metric on $\mathbb{C}$.
- conformal mapping and rational function
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Elementary question on continuity and locally square integrability of a function
- Proving smoothness for a sequence of functions.
- How to prove that $E_P(\frac{dQ}{dP}|\mathcal{G})$ is not equal to $0$
- Integral of ratio of polynomial
Related Questions in INEQUALITY
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- Prove or disprove the following inequality
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- Solution to a hard inequality
- Is every finite descending sequence in [0,1] in convex hull of certain points?
- Bound for difference between arithmetic and geometric mean
- multiplying the integrands in an inequality of integrals with same limits
- How to prove that $\pi^{e^{\pi^e}}<e^{\pi^{e^{\pi}}}$
- Proving a small inequality
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 MAXIMA-MINIMA
- optimization with strict inequality of variables
- Minimum value of a complex expression involving cube root of a unity
- 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?
- Solving discrete recursion equations with min in the equation
- Trouble finding local extrema of a two variable function
- Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?
- Find the extreme points of the function $g(x):=(x^4-2x^2+2)^{1/2}, x∈[-0.5,2]$
- Maximizing triangle area problem
- Find the maximum volume of a cylinder
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?
Yes, it holds, no matter how the $f_t$ are defined. The left hand side cannot be smaller than the right hand side.
Proof: No matter what argument $y\in X$ minimizes the left hand side, you can always make the right hand side at least as small by choosing $y$ as the argument $n$ times in the sum.