What options is available if one wants to minimize a nonsmooth convex function of one variable? Subgradients would work, but there has to be some nice way of utilizing that we're only searching in 1d. Bisection would work, but are there better options?
2026-03-30 13:34:04.1774877644
Minimizing nonsmooth single variable functions?
200 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 NUMERICAL-METHODS
- The Runge-Kutta method for a system of equations
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Is the calculated solution, if it exists, unique?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Minimum of the 2-norm
- Is method of exhaustion the same as numerical integration?
- Prove that Newton's Method is invariant under invertible linear transformations
- Initial Value Problem into Euler and Runge-Kutta scheme
- What are the possible ways to write an equation in $x=\phi(x)$ form for Iteration method?
- Numerical solution for a two dimensional third order nonlinear differential equation
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 NUMERICAL-OPTIMIZATION
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Bouncing ball optimization
- Minimization of a convex quadratic form
- What is the purpose of an oracle in optimization?
- What do you call iteratively optimizing w.r.t. various groups of variables?
- ProxASAGA: compute and use the support of $\Delta f$
- Can every semidefinite program be solved in polynomial time?
- In semidefinite programming we don't have a full dimensional convex set to use ellipsoid method
- How to generate a large PSD matrix $A \in \mathbb{R}^{n \times n}$, where $\mathcal{O}(n) \sim 10^3$
- Gram matrices in the Rayleigh-Ritz algorithm
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?
The Golden section search is guaranteed to converge in your case, and is a bit faster than bisection. I would use this one.
You can also consider Successive parabolic interpolation. Theoretically, it is substantially faster (superlinear convergence) but this method is rarely appropriate on its own: the parabola one gets may lead far from the minimum, especially when your function is not smooth. As the Wikipedia article mentions, this method may be used in alternation with golden section, but you'd have to first consider whether the cost of implementing a complex method like this is justified.