# 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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### Coordinate descent with equality and inequality constraints

I have an intuitive understanding of why the simple method of coordinate descent does not work with linearly coupled constraints such as; $$\min_x\sum_if_i(x_i)$$ $$s.t.$$ $$Ax=b$$ If we try to ...
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### Optimization problem regarding Newton's algorithm

I would want to ask why does Newton's algorithm with Wolfe line search converges to (0,0) no matter where the starting point is?
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### Residual norm of active set method in non negative least squares

I am having trouble with understanding one of the statements in active set methods done for non negative least squares given in Book written by Lawson. The quadratic problem can be written as \begin{...
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### Optimal path around an invisible wall [duplicate]

The Problem On an infinite plane there are two points, $A$ and $B$, a unit distance apart. There is a $50\%$ probability that there is an invisible wall somewhere between the two points. The ...
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### Solving non-linear functional equations numerically by sequence of linear least-squares?

So I am experimenting with a linear systems solver to find new exciting applications for it. While it is possible to play around to solve some of the more basic functional equations, I am trying to be ...
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### Exact and Heuristic Optimization Methods

Could anyone give me a rough classification for which kind of nonlinear- problems can I apply exact optimization methods (such as barrier function) and for which problems heuristic methods (such as ...
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### What exactly are convex constraints?

I haven't been able to find a clear answer to this question, seek an answer from a professor or figure it out myself as I am not a mathematics expert. I used the ...
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### separability of dynamic programming

I am working on some portfolio selection problem and running into this concept. It is stated that "multiperiod mean–variance formulations cannot be solved using dynamic programming due to their ...
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### How to find extreme directions?

objective:min $−3x_1−2x_2−x_3$ The set is : $X=\lbrace (x_1,x_2,x_3):2x_1+x_2-x_3\le2; x_1,x_2,x_3\ge0 \rbrace$ Attempt: $2d_1+d_2-d_3\le0$ (a) $d_1+d_2+d_3=1$ and $d_1,d_2,d_3\ge0$ Since from (...
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### Trust-region method

The question has to do with the trust-region method for unconstrained optimization. I came across it on p.~392 of Linear and Nonlinear Optimization, by Griva, Nash and Sofer. Let $p(\lambda)$ be ...
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### Solution for $\min_{x^Tx=1} x^TAx-c^Tx$

$\min_{x^Tx=1} x^TAx-c^Tx$ looks like a simple QPQC problem. If $A$ is positive semi-definite, can I get the solution by first getting $x=A^{-1}c$ and then projecting $x:=\dfrac{x}{||x||}$ to make ...
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### What is the initial tableau for simplex method with big M method for this problem?

I have an optimization problem with formulation: min f = x1+x2+x3 subject to: x1+2*x2+x3=8 2*x1+x2+x3=12 x1,x2,x3>=0 I should solve it by Big M method. For this I added two extra variables (a1,...
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### Scaling vector-valued objective function for non-linear optimization/minimization

I am trying to minimize a non-linear vector-valued function in MATLAB. As a test case for my code, I try to minimize a function whose solution I know apriori. The problem is that one of the solutions ...
Let $a,b,x$ be vectors in $R^n$, A be a matrix, $c,d \in R, c<d$. Solve the following problem: $$\begin{cases} \text{minimize} \quad (b-Ax)^T(b-Ax)\\ (a^Tx-c).(a^Tx-d) \leq 0 \end{cases}$$ Assume ...