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Questions on linear programming, the optimization of a linear function subject to linear constraints.
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if else statement linear programming
I am trying to work out an if else statement for the following problem, which should be mathematically linear programmed: when both item 1 and item 2 are picked, both their costs are reduced with 20%. ... linear-programming- 1
Assignment Problem (Hungarian): Does increasing a match-specific payoff always make it more likely to be selected?
I'm thinking about the assignment problem for assigning $I$ workers to $I$ tasks (let $I=J$ so there are the same number). Suppose that each possible assignment yields a payoff of $u_{ij}$. I want to ... graph-theory optimization linear-programming operations-research bipartite-graphs- 141
Prove that a standard form primal LP has a nondegenerate optimum if the corresponding dual form LP's optimal is unique & nondegenerate
This is Exercise 4.13 from Bertsimas' Introduction to Linear Optimization. The original question asks that the standard form primal optimum is unique and nondegenerate iff the dual is unique and ... linear-programming duality-theorems- 13
Linear programming by simplex method [closed]
Solve by using simplex method of $\max z=40x_1+88x_2$ Subject to $2x_1+8x_2\leq 60$ $5x_2+2x_2\leq 60$ $x_1,x_2>0$ linear-programming simplex-method- 13
How else can I solve how much decaf and caffeinated coffee should go in my brew?
I want 39mg of caffeine in my 20oz of coffee. blend1 has 9mg / 8oz. blend2 has 91mg / 8oz. it takes me 26g of coffee to produce 20oz. assuming blend1 and blend2 weigh the same, how many grams of ... systems-of-equations linear-programming- 1
My linear program has multiple optimal solutions. I want that corner point at which the value of one of the variables is the maximum?
Is there a way to find the optimal point with this special property in polynomial time? Note that the polytope in the linear program may be unbounded. linear-programming- 46
How do you determine the best solution out of a set of feasible basic solutions/extreme points?
I'm working on one of my exam sets, surrounding linear optimization, and could really use some help. The assignment is essentially $\to$ find the $10$ basic solutions $\to$ find the $5$ feasible ... linear-algebra matrices optimization linear-programming nonlinear-optimization- 11
When does dual simplex algorithm terminate? [closed]
I'm trying to get my head around the dual simplex method. I want to know about the cases where the algorithm terminates. I would like to know what condition must be met to tell if: Prime feasibility ... linear-programming- 1
Parametric linear program with parameterization only in the objective
I am working with a parametric linear program of the following kind where the parameter c is changing: \begin{array}[t]{l} \min c^{\top} x\\ s.t.\\ \quad A x \ge b\\ \quad 0 \le x \le x^{u} \end{array}... linear-programming- 46
How to prove that solution have at most $m$ fractional coordinates
I started to study a bit of mixed linear programming, and I am facing the following exercise that after quite some time I don't know how to approach: Let $A\in\mathbb{R}^{m,n}$, $b\in\mathbb{R}^{m}$, ... optimization linear-programming integer-programming mixed-integer-programming- 870
A minimax optimization with $\ell_p$ constraint
I have a minimax with general $\ell_p$ constraint optimization problem. The objective function is in the following, $$\min_{\mathbf{w} \in \mathbb{R}^d} \mathbb{E}_{(\mathbf{x}, y) \sim P}[\max_{\... optimization convex-optimization linear-programming machine-learning- 11
Matrix optimization - sum of largest element in each column
Feel free to tweek particular expressions if it will make it easier to find a solution. In the end, I will end up with an approximate anyway: $V$ is a given $N\text{ x }m$ complex matrix with columns $... optimization numerical-methods linear-programming nonlinear-optimization- 3,737
Finding all integer solutions for a Linear Program over the Birkhoff Polytope
I have the situation where the Birkhoff Polytope is the space of all valid solutions to a linear function I am interested in maximizing. It is my understanding that, because the vertices of the ... convex-optimization linear-programming birkhoff-polytopes- 21
How to apply matrices to dnd style games
While playing a game, I needed to match 5 Characters to 5 Classes to optimise my team. I've listed the classes each character is suited for: Mage-2,4 Ninja-1,2 Thief-3,5 Warrior-1,2,4 Cleric-2,3,5. I'... linear-algebra matrices linear-programming numerical-linear-algebra- 39
How to linearize z <-> x == y?
I have a constraint that reads $z \iff x = y$ where $z$ is a 0-1 variable and $x,y$ are non-zero, positive integer variables. I'm managed to formulate equivalence going in the right direction, but not ... linear-programming mixed-integer-programming linearization- 245
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