Questions tagged [optimization]

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

775 questions
Filter by
Sorted by
Tagged with
146 views

Gaussian geometry optimisation: molecule is getting dissociated into sub group?

I was trying to optimise CdSe (Cysteine) molecule using a semi-empirical method in Gaussian 09 (and gaussView) for a preliminary study of quantum dots. But it seems as the number of iterations ...
877 views

42 views

Optimisation of purely integer quantity with bound-constraints for a 1D expensive function whose analytical form is not available

I have a computationally expensive objective function, whose analytical form is not available. The only input argument to the objective function is an integer variable. The goal is to compute the ...
79 views

Literature on numerical solving based on multiple meshes?

Consider solving a differential equation system for 1D, 2D, or 3D. It involves various input and output "field" variables, which, more often than not, correspond to various physical quantities ...
123 views

Minimize the number of unique elements in a vector

I was wondering if there is a simple or known way to minimize the number of unique elements in a decision variable (vector). Note that I'm not asking for minimization of nonzero elements (rank ...
142 views

Numerical optimization algorithm with approximated derivatives

Suppose I have a energy functional E depending on X, where X is a N-dimensional real value vector and N could be very large (~=2000). I assume that there exists (at least) a (local) minimizer for E. ...
159 views

Obtaining extra output argument(s) from the objective function used by fsolve in MATLAB

I have a MATLAB code (see below) that employs 'fsolve' from the optimization toolbox for a root finding problem. The bottleneck is that, within the objective function calculation, there is a ...
757 views

How to get multiple solutions for a optimization problem using any kind of software

I have a optimization problem in which the optimal objective value occurs at multiple point in the feasible space. If I run my problem in LINGO software then it gives me the optimal objective value at ...
316 views

Optimisation of matrix exponential

I have a 7000x7000 sparse matrix (scipy), which I want to exponentiate. I've tried using scipy.sparse.linalg.expm, which works quite well for smaller matrices (takes a few seconds for a 1000x1000 ...
29 views

constraint satisfaction via an LD solution

I'm going through the article in the following link lately and one point confuses me a lot. https://arxiv.org/pdf/1509.05001.pdf So, the goal of this paper is to solve the following constrained ...
79 views

14 views

Optimizing estimator of composed functions when function is known

Note: This was cross-posted from comp-sci, as I didn't know this community existed! I have a problem which I'm looking to see if there is literature on: Consider three types of actors, a Director, ...
42 views

Unclear definition of objective function for MPM

While reading this paper on MPM (page 48), the definition of the objective function $E(\boldsymbol v_{\boldsymbol i})$ didn't make sense to me, although I completely understand the definition of (what ...
151 views

lagrangian dual and linear programming

I'm going through an article lately and there is one point which is very confusing. So, we have the following original constrained binary quadratic problem as the following. The pre-assumption of ...
74 views

96 views

Finite difference method for coupled PDEs: optimizing performance (time step, iterations per step)

I'm solving coupled PDEs using finite difference method: Incompressible Navier-Stokes and the divergence-free induction equation (Maxwell's equations) with non-uniform electrical conductivity. The ...
142 views

How to optimally choose points for multivariable Hermite interpolation?

I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input. I would like to create interpolation polynomial for it. In one-dimensional case ...
116 views

preconditioning LBFGS?

I want to minimize an energy of the form $$V_1(\mathbf{x}) + V_2(\mathbf{x})$$ where $V_1$ is much stiffer than $V_2$. When I try to use LBFGS, convergence is extremely slow, as the solution ...
241 views

How to debug a constrained optimization algorithm?

I have implemented a saddle point optimization problem based on the algorithm by Prof. Nesterov, primal-dual[1]. Unfortunately, it doesn't work. It seems it is converging. But unfortunately, not to ...
119 views

reformulating inverse problem as multi-objective optimization

I'm working on an inverse problem for my Ph.D. research, for which I'll write the objective functional as $J(\theta) = E(G(\theta) - u^o)$, where $\theta$ are the parameters, $G$ is the forward map ...
22 views

Break a set of numbers to minimum groups with each having a common divider

I have a set of numbers, all positive, integers obviously, and what I want to do is divide them in the least possible groups with each group having a GCD bigger than 1. The biggest possible number is ...
172 views

105 views

SOCP: Recovering primal from dual

Consider the following second-order cone program (SOCP): $$\begin{array}{rl} \min_x & c^\top x\\ \mathrm{s.t.} & \|A_ix+b_i\|_2 \leq c_i^\top x+d_i \ \forall i \end{array}$$ Suppose I solve ...
197 views

77 views

vectorizing optimization or root finding [closed]

I need to find the roots of a function. I am currently using scipy.optimize.fsolve ...
I am trying to solve a LP in which one of my constraints is of the form $$\frac{A(x)}{B(x)} = 1$$ I transform this constraint into a linear one $$A(x) - B(x) = 0$$ However when CPLEX solves the ...
Consider the following regression model : Y = AX + BU where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$. The matrices X,Y and U are ...