I was reading an article about the robust optimization of the MNL choice model,and in one of its proofs it uses the point that if we're tring to solve the minimun of a quasilinear function ,which is the ratio between two linear functions,then it equals to solve the minimum of this function among all its extreme points.This implies that the optimal point for a quasilinear function lies in its extreme points,but I don't know how to prove this.(Plus,it also says this is a conclusion in the book Convex Optimization by Stephen Boyd an Vadenburghe,but I didn't find)
2026-02-22 19:33:08.1771788788
How to prove that the optimal point for a quasilinear function lies in its extreme points
157 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 ROBUST-STATISTICS
- Least Absolute Deviation (LAD) Line Fitting / Regression
- Calculating Median of grouped frequency distribution using (N+1) rather than (N)
- Robustness of estimators
- Proofs for consistency of estimating equations / M-estimators without a compact parameter space?
- Robust line segment fitting to a digital path
- Stationary of Moving Average Process
- How to prove that the optimal point for a quasilinear function lies in its extreme points
- Estimate scale parameter from 5% contaminated mean-zero normal sample
- How to tell if two samples come from the same probability distribution?
- Multivariate robust estimation for high dimension
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?
Suppose that a minimum is attained in the interior. Then the point at which the minimum is attained can be written as a convex combination of extreme points. The function value at the extreme points is strictly higher than the optimal value (as otherwise such point is also optimal and your procedure would find it). Therefore, there is an upper level set that contains those extreme points but not the optimal point, which contradicts quasiconcavity.