Questions tagged [optimization]

Question 1

Given a set of non-negative real numbers $c_1, c_2, ..., c_N$, and a positive real number $D$ where $D << 1$, find an upper bound of the function: $Q(x_1, x_2, ..., x_N)$ = $\sum_{i=1}^{N}{x_i\,...

Question 2

I am struggling with the modeling of the following optimization problem. \begin{aligned} \min\; z &= \sum_{p\in P}\sum_{s\in S} F_{ps}\,x_{ps} \;+\; \sum_{p\in P}\sum_{c\in C} D_{pc}\,vol_{...

Question 3

Let $u:[0,1]^2\to \mathbb{R}$ be a continuous and differentiable function such that $u(x,x)=0$ for any $x\in [0,1]$, and $\partial u(y,x)/\partial y>0$ for any $x\in [0,1]$ and any $y\in [x,1]$. ...

Question 4

I'm reading the book Convex optimization by Stephen Boyd . In Section 5.9.2 he states (without proof) the Karush-Kuhn-Tucker conditions for an optimization problem with generalized inequality ...

Question 5

Like instead of saying $$\nabla f=\lambda\nabla g$$ can I instead say $$\lambda\nabla f=\nabla g$$ to create an easier system of equations to solve?

Question 6

To implement Benders Decomposition, I am using Yalmip to code my subproblem (SOCP) and to speed up the process, I am using Optimizer to avoid pre-compile for each subproblem. I need to get the dual ...

Question 7

From what I understand: When semidefinite programs (SDPs) don't obey Slater conditions, it is not guaranteed that interior-point methods (IPMs) converge. It appears that facial reduction (FR) ...

Question 8

Given distance $S$, time $T>0$ and bounds on the velocity $v_{\min}<v_{\max}$, $$ \begin{array}{ll} \underset{v:[0,T] \to {\Bbb R}}{\text{minimize}} & \displaystyle \int_0^T f(v(t),e(s(t),t))...

Question 9

From Wikipedia https://en.wikipedia.org/wiki/Rationality#In_various_fields Rationality is a core assumption of game theory: it is assumed that each player chooses rationally based on what is most ...

Question 10

Given distance $S$, time $T > 0$ and bounds on the velocity $v_{\min} < v_{\max}$, $$ \begin{array}{ll} \underset{v : [0, T] \to {\Bbb R}}{\text{minimize}} & \displaystyle\int_0^T f (v(t),t) ...

Question 11

I am trying to solve the following problem: Let's say a "frog" is jumping on the numberline starting at $0$, jumps randomly on every integer from $1,\dots,n$ and then comes back to 0. What ...

Question 12

I am studying a function arising in the analysis of robust aggregation rules in distributed learning, but the question is purely analytical. The function I am facing depends on parameters $a, b > 0$...

Question 13

I'm trying to understand how to correctly choose the next basis after the first iteration in the simplex method. In my problem, I have the following minimization form: $$ \begin{aligned} \min z &= ...

Question 14

I am given 3 radii $r_a, r_b, r_c$ and I want to determine the 3 angles $\phi_a,\phi_b,\phi_c$ for which the area of the triangle defined by $\left(r_a\cos(\phi_a),r_a\sin(\phi_a)\right),\,\left(r_b\...

Question 15

I am in the process of designing a global trajectory program for civil aircraft. Two aircraft depart from their airports, join together to create a formation, then later separate and land at their ...

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Questions tagged [optimization]

Find the maximum of the following function $Q(x_1, x_2, ..., x_N)$ subject to some constraints.

Modeling of an optimization problem

dynamic programming without discounting

Reference Request: Karush-Kuhn-Tucker conditions for convex optimization with generalized inequality constraints.

Can I move the Lagrange multiplier to the other side?

Dual Multiplier by Optimizer (Yalmip) [closed]

Understanding the convergence of SDP facial reduction algorithms

How to solve this kind of constraint optimization problem? [closed]

What is the mathematical definition of rationality in game theory

Solution to a constrained optimal control problem — is $v(t) = \frac{S}{T}$ optimal? [closed]

Maximum Travelling Salesman Problem on the integer line

Maximisation of functions of the form $f(x) = \sqrt{1 - x^2} + (ax+b)x$

Simplex Method - How to know which basis to choose after the first iteration?

Maximizing the area of a triangle

Fermat-Torricelli Weighted Point

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