Tagged Questions

A non-linear optimization problem includes an objective function (to be minimized or maximized) and some number of equality and/or inequality constraints where the objective or some of the constraints are non-linear. Use this tag for questions related to the theory of solving such problems or for ...

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Why does Frobenius norm make BFGS scale-invariant?

On slide 11 here it is claimed that the weighted Frobenius norm leads to a scale-invariant optimization method. Similar claims about this norm can be found throughout the literature see 1,2,3. In ...
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Smallest enclosing cylinder

I have a set of 3D points that approximately lie on a cylinder. This cylinder is straight and can be oriented in any direction. I would like to compute the minimal enclosing cylinder for the set; taht ...
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In my optimization problem, I've a constraint to calculate the average success probability of a path. $x_{i,j}$ is binary variable defined as: \begin{align} \label{eq3:1} x_{i,j} = \begin{cases} ... 0answers 35 views Maximum of Contour Line Consider the potential U(x,y)=ay^{2}+b(e^{x-y}-1)^{2}+c(e^{x+y}-1)^{2} where a, b and c are known constants. I want to move through a contour line of this potential U(x,y)=k, say y=g(x). ... 0answers 66 views How to obtain the optimal Lagrange multiplier vectors if the globally optimal solution for a nonconvex QCQP is found? I am using a black-box solver to solve the following non-convex QCQP to global optimality. \min_x x^TQ_0x + c^T x \\ s.t. \quad x^TQ_1x+c_1^Tx=b_1 \\ Ax=b \\ l\leq x\leq u $$where Q_0 is ... 0answers 550 views SDP relaxation of non-convex QCQP and duality gap Short version Is there a duality gap between a QCQP problem and the SDP problem obtained through Lagrangian relaxation? A paper I'm studying is using this fact, but I cannot achieve the authors' ... 1answer 41 views Non-convex QCQP Consider the following optimization problem:$$\begin{array}{ll} \text{minimize} & \mathbf{x}^{T} \mathbf{A} \mathbf{x}\\ \text{subject to } & \mathbf{x}^{T} \mathbf{P}_i \mathbf{x} > 0, \...
I have this problem and it seems similar to something people must have studied in quadratic optimization/non-convex optimization. $\min_{a,b \in [0,1]^n} a^TM b\\ \text{subject to. } a^TQb\geq \alpha$...