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Questions tagged [optimization]

This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

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Stock Trading algorithm with constraints

Suppose you have an array called prices, where prices[i] denotes the price of a specific stock on the i-th day. Additionally, there are two arrays, ...
Kadanz's user avatar
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15 votes
5 answers
2k views

Ensuring IEEE 754 Compliance and Numerical Precision in C++ HPC Projects

I'm currently engaged in a large-scale C++ HPC project focused on numerical simulation, particularly Finite Element Method (FEM) simulations. Our project spans various Linux-based platforms and ...
René Chenard's user avatar
6 votes
2 answers
293 views

Difficult because non-convex, or some other reason?

In my github project, I have come up with a very simple function that seems to cause problems for all the optimizers I have thrown it at, and I am wondering why. There is an obvious downhill ...
m4r35n357's user avatar
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1 vote
0 answers
47 views

How to solve ADMM Optimization Problem

We are trying to solve the following optimization problem using ADMM: $$ \begin{aligned} & \min _{\left\{y_{i j}^{m}\right\}} \sum_{i \in I_{m}} f_{i j}^{m}\left(y_{i j}^{m}\right)+\sum_{j \in J} \...
ANWESA ROY's user avatar
8 votes
2 answers
700 views

Poor test functions for optimization

I have been looking in detail into one of the many "meta-heuristic" optimization algorithms and became suspicious at how well it appeared to perform (compared to other methods like Nelder-...
m4r35n357's user avatar
  • 245
1 vote
1 answer
76 views

How does the slack variable work in the problem formulation?

Recently I am reading a paper. In it, after they achieve eq(15), which is $$ \operatorname{Tr}(\boldsymbol{Q})-\sqrt{2 \ln (1 / \rho)} \sqrt{\|\boldsymbol{Q}\|_F^2+2\|\boldsymbol{r}\|^2}+\ln (\rho) \...
tyrela's user avatar
  • 133
2 votes
2 answers
108 views

Gradient descent for solving polynomial equations while encouraging variables to be nonzero

I would like to use gradient descent to "randomly sample" solutions to a set of homogeneous polynomial equations. Because the equations are homogeneous, setting all variables to 0 is a valid ...
PPenguin's user avatar
  • 123
0 votes
1 answer
70 views

Why using large bound to supplement inifinity in interior point method can be bad

Here in the documentation of mosek (https://docs.mosek.com/latest/pythonfusion/debugging-numerical.html) we see: Never use a very large number as replacement for infinity . Instead define the ...
Matt Frank's user avatar
0 votes
2 answers
104 views

BFGS Constrained Optimization Failure Due to Precision Loss

I am trying to optimize the following objective function according to some constraints. However, the optimization fails at the first iteration with the message that the desired error was not ...
user47212's user avatar
1 vote
2 answers
412 views

optimizing piecewise linear objective functions (perhaps non convex) with equality constraints

When I do my project, I need to optimize piecewise linear objective functions (perhaps non convex) with equality constraints. The piecewise linear objective function may be not convex like this in the ...
Yiyuan Chen's user avatar
2 votes
1 answer
191 views

Speeding up 3 body problem acceleration calculation

I want to find optimizations to my code for the 3BP, and more specifically computing accelerations. I'm using a data-driven approach, so I have a bodies structure ...
Remeraze's user avatar
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Loop Bounds vs. Iteration Domain in Polyhedral optimization

Context: I was reading a tutorial on polyhedral optimization. But got confused while trying to translate the iteration domain (i.e. loop bound) to set builder notation. Problem Description: A code ...
F.C. Akhi's user avatar
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1 answer
52 views

MIP - Large Piecewise Linear Constraints Over Continuous Intervals

I'm currently trying to run a MIP (have access to both Gurobi and CBC) with a piecewise linear function having ~200 intervals for each of the ~30 x values I have. I am using the standard decomposition ...
davidwashere's user avatar
1 vote
0 answers
28 views

1-dimensional nonlinear global minimization of kepler distance problem

I want to solve the problem to determine the next intersection of a Keplerian orbit with the Sphere of Influence of a celestial body to find the next intersection within one future period of the ...
lamont's user avatar
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dual svm square hinge loss

Let $x_1,\dots,x_n\in \mathbb{R}^n$, $y_1,\dots,y_n\in \{-1,1\}$, $\lambda \ge 0$ and $K$ be the invertible Gram matrix $K=(x_i\cdot x_j)_{ij}$. Consider $$ (P) \qquad \qquad \min_{a\in \mathbb{R}^n} \...
Smilia's user avatar
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0 answers
60 views

Help with inferring Network topology from Spectral templates

I am trying to use matlab and YALMIP to solve a graph learning problem of recovering eigenvalues from the eigenvectors of the covariance of sampled graph signal data. This is to implement the ...
user86422's user avatar
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0 answers
39 views

Methods for delaying the "break" in non-linear least squares optimisation when the step size gets too small?

I am using the Levenberg-Marquardt method for calibration purposes. Typically, the RMSE of my calibration looks like: I want to break the algorithm when the algorithm step-updates start to slow down, ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
2 votes
1 answer
95 views

references for optimization in the context of parameter identification with finite elements

i am performing parameter identification for a non-linear partial differential equation (elasticity) that I solve with finite elements. My optimization problem is a non-linear least squares data-...
Simon's user avatar
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5 votes
0 answers
87 views

optimization scaling techniques

Consider a convex QP of the form $$ \min_x \bigl\{\tfrac12 x^\top Q x + q^\top x : Ax\leq b\bigr\}\tag{P} $$ with dual $$ \min_y \bigl\{\tfrac12 (A^\top y + q)^\top Q^{\dagger} (A^\top y+q) + b^\top y ...
jjjjjj's user avatar
  • 325
0 votes
0 answers
113 views

Why researchers use MATLAB based YALMIP or CasADi for MPC?

I was looking at various research papers and most of the researchers use CasADi, YALMIP, MPCTools to implement MPC. My question is "Why researchers use MATLAB based YALMIP or CasADi for MPC ...
Khalid Umer's user avatar
3 votes
1 answer
150 views

Role of rotation's pivot point in optimization?

In this paper, the authors describe how to use locally rigid transformations (sampled on nodes in space) to deform mesh vertices. In the paper, rotations are relative to the pivot point, which ...
jordi's user avatar
  • 31
0 votes
0 answers
58 views

PETSc non-linear solvers (SNES): specifying single Eval & Jacobian function

The PETSc documentation example of a non-linear solver call has the user provide separate functions for the Jacobian and function evaluations: ...
Sardine's user avatar
  • 378
1 vote
1 answer
117 views

Improvement to naive gradient descent implementation for the Thomson problem

I have a Python program (available on github) that uses naive gradient descent to find approximate solutions to the Thomson Problem. It works surprisingly well, but I've been wondering if there's a ...
Martin C.'s user avatar
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38 votes
10 answers
9k views

stupid + stupid = brilliant in scientific computing

I'm interested in examples of very effective methods in scientific computing that are the sum or naive combination of very ineffective or bad ones.
Daniel Shapero's user avatar
2 votes
2 answers
110 views

Automatic Differentiation In the Presence of Jump Points

I have a complex monte-carlo cashflow model that traditionally uses the finite difference (FD) method to calculate its derivative at any given point. To improve model performance, I coded forward-mode ...
Mild_Thornberry's user avatar
1 vote
2 answers
157 views

Are there good block sparse matrix solver libraries?

There are some great libraries with linear solvers for sparse matrices - SuiteSparse is the obvious one. The methods work on sparse matrices with scalar entries. However, often in optimization ...
user664303's user avatar
3 votes
0 answers
60 views

What 2nd-order optimization algorithms have convergence guarantees for strictly- but not strongly-convex problems?

A function $f$ is strictly convex if $$f((1 - \lambda)x + \lambda y) \le (1 - \lambda)f(x) + \lambda f(y)$$ with equality if and only if $x$ and $y$ are equal. This implies that the second derivative ...
Daniel Shapero's user avatar
1 vote
1 answer
60 views

Optimization: Find minimizer along linestring

Given some function f(x) and a set of points A representing a linestring (or polygonal chain), I am searching for the point on ...
Citizen3011's user avatar
1 vote
1 answer
44 views

Name this optimum-within-convex-hull algorithm: State is a convex combination of hull vertices; Nonnegativity ensured by reparameterization

I'm looking for the "official" name(s) for a procedure for optimizing a convex loss function over a convex subset. This seems to be a default/naïve algorithm that folks come up with before ...
MRule's user avatar
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1 vote
0 answers
52 views

Beyond the LP relaxation of binary least squares

I have a binary quadratic program with a convex objective function, of the form, \begin{align} \text{minimize}\;\;& x^tAx+b^tx\\ \text{subject to}\;\;& x_i\in\{0,1\} \end{align} where $A$ is ...
Set's user avatar
  • 503
5 votes
3 answers
419 views

Packages suitable for numerical optimization of functions with discontinuous gradient at the point of minimum

Are there packages for numerical optimization in julia or python, or in any other system for scientific computing, capable of taking into account the discontinuity of gradient at the minimum point? ...
Gec's user avatar
  • 153
1 vote
0 answers
66 views

min(f(x)) is convex or concave based on type of f(x)

i have f(x) that is concave function. My question is g=min(f(x)) is concave or convex? And max(g) is concave or convex? there is a theorem for this?
Maria's user avatar
  • 11
1 vote
1 answer
115 views

Possible bug with scipy.optimize SHGO sobol: TypeError: <lambda>() takes 1 positional argument but 3 were given

I have been trying to perform some global optimization with SciPy optimizer SHGO and I've had issues with the sampling method 'sobol'. Specifically, I get an error ...
Sasche's user avatar
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0 votes
0 answers
54 views

Solving a minimization problem without flattening inputs?

I am reading this paper on improving time steps for solving simulation problems: https://www.math.ucla.edu/~jteran/papers/GSSJT15.pdf The authors developed this energy function: $$E(x) = \frac{1}{2\...
Makogan's user avatar
  • 263
0 votes
0 answers
12 views

Estimating/Tuning a Coefficient from a Quadratic Programming Objective Function so Optimal Solution Reflects Data

I am working on a problem that is a modified version of a two-knapsack knapsack problem. I am able to find the optimal choices by using Gurobi. However, I would like to estimate a coefficient that is ...
Jack Keefer's user avatar
0 votes
0 answers
59 views

Rank-one updates for symmetric matrix eigen-system

Are there existing implementations for rank-one updating of symmetric matrices eigensystems? This is the mathematical statement of the problem. Let $S=QDQ^T$ $$S + vv^T = QDQ^T +vv^T = Q_{new}D_{new}...
Sandeep Mukherjee's user avatar
0 votes
1 answer
59 views

The row loss gradients

Suppose the original loss function is $$\min_{\mathbf{V}}\frac{1}{2}\|\mathbf{V} - Q(\mathbf{V})\odot\mathbf{U}\mathbf{E} - \beta Q(\mathbf{V})\mathbf{V}\|_2^2$$ where $\odot$ denotes the element-wise ...
Zuba Tupaki's user avatar
1 vote
1 answer
232 views

Python libraries for larges scale optimization/rootfinding

I have been dealing with the standard libraries of scipy.optimize for rootfinding and optimization problems, but the problems i want to solve are very large, which makes the standard solvers run out ...
Klaus3's user avatar
  • 133
1 vote
0 answers
63 views

Gradient based optimization involving a black box function where gradients (not the objective) are approximated using a surrogate model

Can we use gradients of surrogates of a black box function and the actual function evaluation for optimization involving an expensive black box simulation? Is there any merits to it?
almostKapil's user avatar
1 vote
0 answers
41 views

Where to find datasets to research the optimal parameter search space for HPC systems? [closed]

I am a student researcher who is new to the HPC domain. I have recently taken a project where I am working on optimizing the parameter search space (both application level and hardware level ...
Abrar Hossain's user avatar
3 votes
0 answers
63 views

When is it worth it to use the dual simplex method with warm starts?

Let's say I have a linear program that incurs a series of slight changes to it, so I want to warm-start it. I've read various things that recommend using the dual simplex algorithm over the primal ...
paulinho's user avatar
  • 131
2 votes
0 answers
126 views

Is the Hessian of the strain energy of a hyperelastic material positive definite in general

Is the spatial second derivative of the strain energy of a hyperelastic material positive definite in general? If this is not a general property of hyperelastic materials are there techniques for ...
Olumide's user avatar
  • 265
2 votes
0 answers
98 views

Can we get the exact solution of large-scale quadratic programming problems (quadratic objective, linear inequality constraints) using KKT condition?

Crossposted at MathOverflow Consider a quadratic programming problem with the following format: $$ \text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\ $$ $$ \text{s.t.} Ax\leq b, \\ x\geq 0 $$ where $D$ is a $...
ximeng fan's user avatar
5 votes
1 answer
210 views

How to optimize an approximated matrix multiplication?

[UPDATING] The old one is a simplified version of the current one. Here is a solution based on the answer proposed by professor Bangerth down below. To describe what I am trying to do, first rewrite ...
Zuba Tupaki's user avatar
1 vote
0 answers
40 views

step size cycling in semismooth newton for convex problem

I am using backtracking linesearch to globalize a (semismooth) newton solver to minimize a (strongly semismooth) strongly convex function , and I am observing something strange (which may be a bug). ...
jjjjjj's user avatar
  • 325
1 vote
0 answers
47 views

Vehicle passenger assignment with capacity constraint

Problem Background I'm trying to find a solution to the following passenger matching problem: The network is represented by graph $G=(V,E)$. $V$ is the set of nodes/stations. $p_{ij}$ is the profit of ...
Corey's user avatar
  • 11
1 vote
0 answers
51 views

function optimization using reinforcement learning

I'm regular with optimization process, but this time, I would like to optimize a multiobjective function with reinforcement learning, using python. Of course I already have some testing functions (...
lelorrain7's user avatar
4 votes
1 answer
241 views

Selecting most points from a set of points with distance constraint

I am looking for an algorithm to select the largest subset of $M$ points from a set of $N$ points ($M < N$) such that no point is within a certain minimal distance d to any other point in $M$? I ...
doom4's user avatar
  • 143
3 votes
0 answers
58 views

Adjoint method for imaging with an "analytical" forward model

I am working on tomographic image reconstruction (radar regime) of the dielectric properties of objects. As part of my work, I have programmed a ray tracer. This ray tracer is, in a way, purely "...
DominikR's user avatar
2 votes
0 answers
98 views

Parameter choice rules for L1 regularization?

I am solving an L1 regularized least squares of the form like: $$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \...
yourds's user avatar
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