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Question 1

2votes

1answer

83views

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

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 &= ...

Ben Shaines

241

askedyesterday

Question 2

1vote

1answer

84views

Maximizing the area of a triangle

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\...

Manfred Weis

252

asked2 days ago

Question 3

0votes

0answers

49views

Fermat-Torricelli Weighted Point

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 ...

Daniel Kowalski

1

askedNov 24 at 18:04

Question 4

1vote

1answer

46views

Linearization Question for max-min|x| Bi-level Optimization Problem

I'm currently working on a bi-level optimization problem with the following structure:max min |x|I attempted to linearize this problem using the following approach:Introduce an auxiliary variable ...

xiusi wang

13

askedNov 24 at 17:56

Question 5

0votes

0answers

46views

How to see $x_1\geq 0$ in the primal implies $p' A_1 \leq c_1$ in the dual, when there are no other constraints than just $x_1\geq 0$?

I understand why the constraint $x_1 \geq 0$ in the primal, implies $p'A_1 \leq c_1$ in the dual in the presence of a constraint involving an $A$ and a vector $b$ in the primal ($A_1$ being the first ...

niobium

1,369

askedNov 22 at 10:17

Question 6

-1votes

0answers

35views

When does an optimization problem that is "worth solving" also satisfy strong duality?

I want some minimalistic/easy to remember statements that relate someone's willingness to solve an optimization problem with the strong duality property of that problem. Of course, you would only want ...

Your neighbor Todorovich

8,711

askedNov 21 at 15:15

Question 7

1vote

0answers

47views

+100

Solving for a diffraction grating's orientation and surface periodicity from its diffracted beams, can the problem be inverted?

Background:Below is a calculation of the diffracted wavevector $\mathbf{k_1}$ from an initial wavevector $\mathbf{k_0} = -k_0 \mathbf{\hat{z}}$ incident on a planar surface with normal $\mathbf{\hat{...

uhoh

1,897

askedNov 20 at 12:17

Question 8

0votes

0answers

23views

Max–min assignment on a DAG when nodes have candidate values with compatibility constraints

I have a DAG where every node has a (usually small) set of candidate integers. A candidate a is compatible with b if (a | b) or (b | a). For every root I want to choose one candidate per node to ...

user5109988

81

askedNov 20 at 8:58

Question 9

0votes

1answer

23views

Does block coordinate descent lead to a constrained critical point?

Let $f:\mathbb{R}^N\to[0, \infty)$ be a non-convex function of $w\in\mathbb{R}^N$ for $N\in\mathbb{N}$. Suppose the entries in $w$ can be partitioned into two vectors $u\in\mathbb{R}^m$ and $v\in\...

Benjamin Tennyson

105

askedNov 17 at 18:08

Question 10

0votes

1answer

95views

How many big and small marbles are not used?

Translating to English from a non-English physics book about measurements:Anif has $8$ big marbles and $15$ small marbles. The weight of the big and small marbles are $37.5$ and $12.5$ respectively. ...

user516076

2,491

askedNov 17 at 0:53

Question 11

4votes

1answer

78views

Optimal strategy for combinatorial marble-drawing game

You have $a$ amber, $b$ bronze, and $c$ crimson colored marbles in your hand, with $a\geq b\geq c$. An exact copy of this set of marbles is in a bag. Every turn, you select a marble from your hand to ...

CosmicOscillator

2,324

askedNov 16 at 2:38

Question 12

1vote

1answer

47views

It seems that the definition of dual problem in Boyd & Vandenberghe does not apply to SVM

In Section 5.2 of Boyd & Vandenberghe's Convex Optimization, the dual problem given a primal problem with only inequality constraint is,$$ \max \quad g(\alpha) \\ \text{ s. t.} \quad \alpha \...

Your neighbor Todorovich

8,711

askedNov 15 at 13:56

Question 13

5votes

4answers

377views

Minimizing $\sum\limits_{i=1}^n (x_i^3 - x_i^2)$ subject to $\sum\limits_{i=1}^n x_i = S$

The following is an algebraic problem I encountered in my research direction.Let $x_1, \dots, x_n \ge 0 $ be non-negative real numbers satisfying $\sum\limits_{i=1}^n x_i = S,$ where $S \ge 0 $ is ...

luyao

89

askedNov 13 at 14:37

Question 14

0votes

1answer

132views

Find the maximum and minimum values of $a+b+c$ in the equation $x+y+a+b+c=2016$

Suppose $a,b,c,x,y$ satisfy $0\le a\le x\le b\le y\le c$ and $x+y+a+b+c=2016$.a) Find the maximum value of $a+b+c$ and find all values of $a,b,c,x,y$ that take this maximumb) Find the minimum value ...

John O'neil

1,063

askedNov 13 at 9:33

Question 15

0votes

0answers

27views

Active set method applied on the min-flow problem

Hello — I’m implementing an active-set method to solve a convex quadratic min-cost flow problem as a project university (I’m studying Computer Science, not Mathematics) of the form:$min\{x^TQx + qx: ...

Dante

1

askedNov 12 at 16:53

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Stack Exchange Network

Questions tagged [optimization]

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

Maximizing the area of a triangle

Fermat-Torricelli Weighted Point

Linearization Question for max-min|x| Bi-level Optimization Problem

How to see $x_1\geq 0$ in the primal implies $p' A_1 \leq c_1$ in the dual, when there are no other constraints than just $x_1\geq 0$?

When does an optimization problem that is "worth solving" also satisfy strong duality?

Solving for a diffraction grating's orientation and surface periodicity from its diffracted beams, can the problem be inverted?

Max–min assignment on a DAG when nodes have candidate values with compatibility constraints

Does block coordinate descent lead to a constrained critical point?

How many big and small marbles are not used?

Optimal strategy for combinatorial marble-drawing game

It seems that the definition of dual problem in Boyd & Vandenberghe does not apply to SVM

Minimizing $\sum\limits_{i=1}^n (x_i^3 - x_i^2)$ subject to $\sum\limits_{i=1}^n x_i = S$

Find the maximum and minimum values of $a+b+c$ in the equation $x+y+a+b+c=2016$

Active set method applied on the min-flow problem

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