Related papers: Price of Coupling in Multilevel Linear Programming
We study the restricted inverse optimal value problem on linear programming under weighted $l_1$ norm (RIOVLP $_1$). Given a linear programming problem $LP_c: \min \{cx|Ax=b,x\geq 0\}$ with a feasible solution $x^0$ and a value $K$, we aim…
In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…
We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…
We consider the symmetric Toeplitz matrix completion problem, whose matrix under consideration possesses specific row and column structures. This problem, which has wide application in diverse areas, is well-known to be computationally…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…
Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…
We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer…
Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…
In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…
Given a capacitated communication network $\mathcal{N}$ and a function f that needs to be computed on $\mathcal{N},$ we study the problem of generating a computation and communication schedule in $\mathcal{N}$ to maximize the rate of…
We present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
We study the Maximum Budgeted Allocation problem, which is the problem of assigning indivisible items to players with budget constraints. In its most general form, an instance of the MBA problem might include many different prices for the…
We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest…