When is
\begin{equation} \min_X \max_Y f(X,Y) \end{equation}
globally solvable? I.e., when can we find global solution for the optimization problem?
I am not looking for reformulations. Is it only when $f$ is concave in $Y$ and convex in $X$?
2026-03-25 09:44:43.1774431883
Global min-max optimization
578 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in MULTIVARIABLE-CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- $\iint_{S} F.\eta dA$ where $F = [3x^2 , y^2 , 0]$ and $S : r(u,v) = [u,v,2u+3v]$
- Proving the differentiability of the following function of two variables
- optimization with strict inequality of variables
- How to find the unit tangent vector of a curve in R^3
- Prove all tangent plane to the cone $x^2+y^2=z^2$ goes through the origin
- Holding intermediate variables constant in partial derivative chain rule
- Find the directional derivative in the point $p$ in the direction $\vec{pp'}$
- Check if $\phi$ is convex
- Define in which points function is continuous
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 $x_1^2+x_2^2 \le 4$
Related Questions in DUALITY-THEOREMS
- Computing Pontryagin Duals
- How to obtain the dual problem?
- Optimization problem using Fenchel duality theorem
- Deriving the gradient of the Augmented Lagrangian dual
- how to prove that the dual of a matroid satisfies the exchange property?
- Write down the dual LP and show that $y$ is a feasible solution to the dual LP.
- $\mathrm{Hom}(\mathrm{Hom}(G,H),H) \simeq G$?
- Group structure on the dual group of a finite group
- Proving that a map between a normed space and its dual is well defined
- On the Hex/Nash connection game theorem
Related Questions in GLOBAL-OPTIMIZATION
- $2$-variable optimization problem — global maximum
- Can basin-hopping be applied for global constrained optimization?
- How to find potential near-optimum clusters after random sampling?
- Any comprehensive books on global smooth optimization?
- Is there any algorithm to find the global minimum for the quasi-convex optimization?
- Global optimization
- Rigorous global optimization
- Do initial parameters in this global optimization problem matter?
- $f(\theta)<f(\theta^*)$ $\forall \theta\in \Theta$ implies $\theta^*=argmax_{\theta\in \Theta}f(\theta)$
- how to find global minimum and max over set s
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?
There are primarily two things -
A convex domain enables us to make strong comments regarding the global maxima and minima.
The objective function will have a maximum iff it is concave in the domain and min iff it is convex. This statement can be made if we have been given that the domain in convex.