Questions tagged [nonconvex]

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Black box optimization

I have a simulation which gives a scalar result depending on the choice of some continuous design variables. I am trying to minimize the output of the simulation. As a first step, I want to study the ...
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37 views

Convergence of Truncated Newton for non-convex Hessian

I was wondering if anyone could enlighten me about the convergence properties of the truncated newton method in case of a non-positive definite hessian $\nabla^2 f = H$. From the Book 'Numerical ...
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109 views

Proving convexity of Frobenius norm and correlation function formulations of an optimization problem

I have been working on formulating my requirements in the form of an optimization problem in a multi-output regression setting. Firstly, I would like to make the variables I used in the problem and ...
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73 views

Global optimization with known distributions of some variables

I'm solving simple single-objective multidimensional global optimization problem using various stochastic algorithms like Monte-Carlo, GA and other evolutionary approaches. The task is formulated as ...
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98 views

non convex, non linear optimization involving matrix differential equation solution

I'm trying to develop an inferential procedure for a multivariate dependent Markov process. Basically, the procedure could be considered as a non linear regression, with a known dependence structure ...
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352 views

Finite difference scheme for solving nonlinear least-squares problem

I am dealing with following problem: $$ \min_{u,\gamma}\Bigg\{ \frac{1}{1000} \iint_{S_2} {\gamma (x,y)^2 dxdy} + \iint_{S_2} {[u(x,y) - u_0 (x,y)]^2 dxdy} + \iint_{S_2} {[\Delta u(x,y) - \gamma (...
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70 views

Ramp least squares estimation

With some given $s$ value, let \begin{equation} \begin{aligned} h(\beta)&=\min(\sum_{i=1}^n(Y_i - X_i\beta)^2, s)\\ &=\sum_{i=1}^n(Y_i - X_i\beta)^2-\max(0, \sum_{i=1}^n(Y_i - X_i\beta)...
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84 views

Best optimizer for unconnstrained non-convex nonlinear least-square optimization problem?

I am looking for a very good optimizer to the following problem: $$\min_{P,\Theta}\lVert APD(\Theta)P^{-1} -B \rVert_F$$ where $A,B \in \mathbb{R}^{n\times m}$, $P \in \mathbb{R}^{m\times m}$, $D\in \...
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38 views

Efficient numerical optimization of an “almost separable” function

I have come across an optimization problem with the following objective function: $$f(x_0,y_0,z_0,x_1,y_1,z_1,...,x_N,y_N,z_N) = \sum_{i=0}^N f_i(x_i,y_i,z_i, \alpha(x_{i+1}-x_i) + \beta(y_{i+1}-y_i))...
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71 views

Minimizing the products of variables

My problem Maximize $$\min_{i} \{\ c_i \cdot \prod_{j \in A(i)} {x_{j}} \prod_{j \in B(i)} {y_{j}} \} $$ Subject to \begin{align} &\sum_{j \in C(k)} x_{j} = 1,\ \forall k \\ &l \leq x_{j}...
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245 views

Constrained optimization: Stationary point vs. Nash point

1s question: definition of stationary point for constrained optimization As far as I know, a stationary point of a constrained optimization problem is a stationary point of the Lagrangian (that has ...
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146 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 ...
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258 views

Numerical solution of non-linear advection equation other than inviscid burgers

I am solving a non-linear advection equation of the form $u_t + f(u)_x = 0$ where $f(u)$ is a complicated function of $u$. I am solving this equation using a first order fully implicit scheme (...
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139 views

Minimization of the sum of convex function and non-linear non convex function

I'm trying to minimize the unconstrained scalar sum of a quadratic convex function (to which a convex optimizer is readily applied) and a non-linear and non-convex function which is differentiable. ...
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363 views

Solving a non-convex optimization problem using fmincon

I am trying to solve a non-convex optimization problem using fmincon(). At each iteration, I am iteratively looking for the optimum value and when the termination ...
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36 views

Minimizing the ratio of two specific non negative quadratic convex functions

$F$ is $m\times m$ diagonal, with real non negative elements $D$ is $n \times m$ complex $P$ is $n \times 1$ complex $A$ is $m \times 1$ complex. Minimize $\Gamma(A)$, with respect to $A$. $$\...