Related papers: Exact Objective Space Contraction for the Preproce…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…
As the demand for computational power grows, optimizing code through compilers becomes increasingly crucial. In this context, we focus on fully automatic code optimization techniques that automate the process of selecting and applying code…
Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given \xi_i > 0. This problem, with random…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
Recent advancements in quantum annealing hardware and numerous studies in this area suggests that quantum annealers have the potential to be effective in solving unconstrained binary quadratic programming problems. Naturally, one may desire…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
In the bi-objective branch-and-bound literature, a key ingredient is objective branching, i.e. to create smaller and disjoint sub-problems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…