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Infinite Linear Programming

I'm trying to prove optimality for a continuous linear program. That is, I have a linear program with an uncountable number of variables and constraints. I'm not sure how to demonstrate feasibility ...
Carrie Nuttall's user avatar
3 votes
0 answers
282 views

Continuum of Lagrange multipliers, duality gap, and minimax theorem

Suppose I have a linear optimization problem involving random variables on some (infinite) probability space $\Omega$. For example, need to maximize expectation $E[Q]$ of random variable $Q$ subject ...
Bogdan's user avatar
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2 votes
1 answer
877 views

Interpreting mincost flow dual variables

Consider the task of finding flow of size $b$ with minimum possible cost. It may be formulated as linear programming in a following way: $$\boxed{\begin{gather} \min\limits_{f_{ij} \in \mathbb R} &...
Oleksandr  Kulkov's user avatar
2 votes
0 answers
66 views

Proving the existence of a dual for an infinite linear program

I am concerned with proving the existence of the dual of an infinite linear program. In addition to the writings of Rockafellar, Luenberger, and Boyd & Vandenberghe on: subdifferentials, Legendre-...
teddy's user avatar
  • 121
1 vote
0 answers
187 views

Strong Duality of Mixed Integer Linear Program

The problem at hand is to optimize a mixed-integer linear program closely related to the maximum flow problem. I would like to reformulate the problem with its dual and I'm concerned with the ...
Amitai G's user avatar