# Questions tagged [constrained-optimization]

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### Fast approximate solver for vehicle routing problem

I need to solve capacitated asymmetrical vehicle routing problem with time windows on ~30k points. Time limits for calculations are 2 hours. I've tried using Clarke and Wright savings algorithm, it is ...
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### Find a vector B that minimizes |W-A*B|

I want to find a candidate vector $B$ that $$\min|(W - A_i * B_i)|$$ $$a_i > 0,\ A_i=\{a_0,...,a_i\},\ B_i=\{-1,0,1\}^i$$ For example, given $$W = 0.6,\quad A_4 = [0.1, 0.2, 0.4, 0.7]$$ one ...
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### 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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### Why would BFGS converge to a local minima of a non-convex function but maintain a large gradient?

I'm using BFGS to optimize a smooth but non-convex function $f$ that is computed by a simulation. The simulation also gives me a semi-analytical gradient $g$, which is verified by the numerical ...
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### Augmented Lagrangian Techniques Frank-Wolfe Algorithm [python]

I'm trying to solve the convex quadratic problem (quadratic min cost flow problem) using the Frank-Wolfe algorithm. $$\min\{x^TQx+qx: Ex=b,\quad 0\leq x \leq u\}$$ The standard algorithm is okay ...
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### Biconvex problem whose objective function depends on only one variable

I am solving the following biconvex problem: $$\min_{x,y} f(y)$$ $$s.t. ~~ g(x) \leq 0$$ $$~~~~~h(x,y) = 0$$ $$x \in X, y \in Y$$ where $X$ and $Y$ are compact convex sets, $g(x)$ and $f(y)$ are ...
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### Formulate and solve a simple conic programs in cvxpy language [closed]

Let $r,\epsilon > 0$ and $a, b \in \mathbb R^n$ with $\|a\|_2 \le r$. Define $C(a) := \{x \in \mathbb R^p | \|x+a\|_2 \le r,\;\|x\|_\infty \le \epsilon\}$, and assume it is non-empty. Question (A)...
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### Question about strange outputs from the CVXPY solver

I am familiarizing myself with CVXPY, and encountered a strange problem. I have the following simple toy optimization problem: ...
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### Techniques to remove a function from Levenberg-Marquardt when it is against box constraints

I have a somewhat large (20+ dimensional) root finding problem that I'm solving with Levenberg-Marquardt. One of the functions has box constraints on [0, 2]. When it is against those bounds it will ...
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### How to find two points within defined region in this constrained optimization problem?

I am doing a project related to robotics where I am using fmincon function from matlab to minimize the distance between the points ...
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### Solution of constrained system of ODEs

Can someone point me in a direction to solve this kind of integral constrained system of ODEs. \begin{align} &\int_0^{1/2}\dot{y}^2(t)=p\\ &2\lambda_1\ddot{y}(t)+\pi cos(\pi y(t))=0\\ &y(...
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### Can LINCS algorithm be used for colliding molecules?

Supposing that one molecule is static and one is dynamic, can the dynamic one be solved with LINCS for its shape (angle, bond length) constraints and also keep collisions with static molecule off, ...
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### Improve optimization speed for a set of similar problems: Quadratic programming with a warm start

I am repeatedly solving quadratic program, $x^T Q x$ with time dependent linear constraints $Ax=b_t$. Dimension of $x$ is around 10000 and there are around 50 constraints. I want to solve the ...
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### sum of absolute difference constraint in optimization problem

I am writing a model for an optimization problem. I need to write the following constraint: $$\sum^{N - 1}_i \lvert (a_i - a_{i+1}) \rvert \leq 2\, .$$ How to write this constraint (or linearize)? ...
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### Interpolation by Solving a Minimization Problem (Optimization)

I will try to give the motivation behind this problem and later the math formality. Given a grayscale image (1 Channel - $M \times N$ Matrix). Someone marks some pixels as anchors. Now, you need to ...
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### Ways to speed up solving an LP with Google's ortools

I'm having an issue solving an LP of the form: $$\min z = c^Tx$$ $$\text{s.t.}$$ $$Ax \geq b$$ $$x\geq p$$ $1 \leq a_{ij} \ll b_i$, $p \leq 0$, and $c \geq 0$ The specific problems I'm running into ...
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### How does fmincon in MATLAB calculate gradients?

I am trying to solve numerically a constrained optimisation problem in MATLAB, and I am wondering how the fmincon function calculates gradients when one isn't ...
I have a 7-14 dimensional piecewise linear cost function I'd like to minimize with two quadratic terms of the form: $$f(X) = X^tCX + d \sum_i |x_i-x^*_i|^2 + \sum_i P_i(x_i-x^0_i)$$  \sum_i x_i ...