Constrained optimization Definition and 20 Threads

For this problem I am using 'cvxpy' library and using a set of constraints to optimize the value of t and X.

I'm reading the book Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville, and currently reading this chapter on numerical methods--specifically, the section on constrained optimization. The book states the following. Suppose we wish to minimize a function...

Hello, I am using the Lagrange multipliers method to find the extremums of ##f(x,y)## subjected to the constraint ##g(x,y)##, an ellipse. So far, I have successfully identified several triplets ##(x^∗,y^∗,λ^∗)## such that each triplet is a stationary point for the Lagrangian: ##\nabla...

Summary:: Hi, this is an exercise from an algorithm course. I have been trying for hours but I have no successful ideas on how to solve it. I can only understand that DP is the correct approach, since Greedy method does not work. Suppose you have *n* friends that wants to give you an amount of...

Note this is in our Lagrangian Mechanics section of Classical Mechanics, so I assume he wants us to use Calculus of Variations to solve it. The surface area is fixed, so that'll be the constraint. Maximizing volume, we need a functional to represent Volume. This was tricky, but my best guess for...

Hi all, I was working on a problem using Euler-Lagrange equations, and I started wondering about the total and partial derivatives. After some fiddling around in equations, I feel like I have confused myself a bit. I'm not a mathematician by training, so there must exist some terminology which...

I have seen the implementation of L-BFGS-B by authors in Fortran and ports in several languages. I am trying to implement the algorithm on my own. I am having difficulty grasping a few steps. Is there a worked out example using L-BFGS or L-BFGS-B ? Something similar to...

Problem: Fix some vector ##\vec{a} \in R^n \setminus \vec{0}## and define ##f( \vec{x} ) = \vec{a} \cdot \vec{x}##. Give an expression for the maximum of ##f(\vec{x})## subject to ##||\vec{x}||_2 = 1##. My work: Seems like a lagrange multiplier problem. I have ##\mathcal{L}(\vec{x},\lambda)...

Homework Statement There is a typo in the problem, ”R > Σ n i=1 σi − n max 1≤i≤n σi” which should be R > n max (1≤i≤n) σi − (Σ n i=1 σi ) Homework EquationsThe Attempt at a Solution Not sure where to go with part B or where to start...

Perhaps the title says it all, but I should expand it more, I guess. So I am trying to explore more about constrained optimization. I noticed that there are very little to no formal (with examples) discussions on algorithms on nonlinear constrained optimization in the internet. They would...

Hi all, I am looking for an efficient solution to solve the following problem. Can anybody help? Assume a set S of elements ki and a set V of possible groupings Gj. A grouping Gj is a subset of S. Associate a weight wij to each mapping ki to Gj. The weights are infinite if ki ⊄ Gj, and finite...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Homework Equations Constrined optimzation The Attempt at a Solution ("o" means dot product) Let M={x|Ax=c} and f(x)=(1/2)x o Qx - b o x Suppose x0 is a local min point. Suppose, on the contrary, that x0 is NOT a global min point. Then there must exist a...

Homework Statement Hello! I'm having some difficulty getting the objective function out of this question, any help/hints would be appreciated >.< Company A prepares to launch a new brand of tablet computers. Their strategy is to release the first batch with the initial price of p_1 dollars...

Hi all, I have this kind of optimization problem: Variable to control: A=A=[a1;a2;...;am] objective function to minimize: L=A*TL where L is a scalar T is a matrix [1,m] TL is a matrix [m,1] constrain: Dt>Dtv where: Dt=[dt1;dt2;...;dtn] Dtv=[dtv1;dtv2;...;dtvn] is a...

Hi all, I am working on a project and stuck at the following problem. Find vector x_{n\times 1} which minimizes the function f(x) = \sum_{i}^{n}x_{i}^{2} subject to the linear equality constraint [A]_{m\times n} x_{n \times 1}=b_{m\times 1} with m\leq n The function f(x) trivially...

Hi, I'm trying to do a constrained optimization problem. I shall omit the details as I don't think they're important to my issue. Let f:\mathbb R^n \to \mathbb R and c:\mathbb R^n \to \mathbb R^+\cup\{0\} be differentiable functions, where \mathbb R^+ = \left\{ x \in \mathbb R : x> 0...

hi i want to find values of a,b,c such that.. Minimize (a+b+c) constrained to (x-a)^2 + (y-b)^2 + (z-c)^2 less than equal to R(z) (x-a)^2 + (y-b)^2 + (z-c)^2 greater than equal to r(z) can anyone help me solving this?? which method should b used for better computation??

I'm trying to find the regular parallelepiped with sides parallel to the coordinate axis inscribed in the ellipsoid x[2]/a[2] + y[2]/b[2] + z[2]/c[2] = 1 that has the largest volume. I've been trying the Lagrangian method: minimize f = (x)(y)(z), subject to the constraint (x[2]/a[2] + y[2]/b[2]...

Im not sure if this is the right place, but I have an optimization problem where I assume we are supposed to use the Lagraingian method: Consider the labour supply problem for an individual over an entire year. Suppose the individuals utility is described by the function U = (C^0.5) x...