(Mixed) Integer Nonlinear Programming

Benchmarking Piecewise Linear Relaxations for MINLPs: A Computational Study Based on the Open-Source Framework PWL-T-Rex

Categories (Mixed) Integer Nonlinear Programming Tags , , ,

Solving mixed-integer nonlinear problems by means of piecewise linear relaxations has emerged as a reasonable alternative to the commonly used spatial branch-and-bound. These relaxations have been modeled by various mixed-integer models in recent decades. The idea is to exploit the availability of mature solvers for mixed-integer problems. In this work, we implement a framework that … Read more

A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming

Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Second-Order Cone Programming Tags , , , ,

One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more

Information Complexity of Mixed-integer Convex Optimization

Categories (Mixed) Integer Nonlinear Programming, Convex and Nonsmooth Optimization, Convex Optimization Tags , , ,

We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) as the gap between the lower and upper bounds. This is derived … Read more

Switching Time Optimization for Binary Quantum Optimal Control

Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications, Control Applications Tags , ,

Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical … Read more

Efficient Cross-Validation for Sparse Linear Regression

Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To choose hyperparameters that control the sparsity level and amount of regularization, practitioners commonly use k-fold cross-validation. However, cross-validation substantially increases the computational cost … Read more

Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations … Read more

Using dual relaxations in multiobjective mixed-integer quadratic programming

Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values … Read more

Compressed Sensing: A Discrete Optimization Approach

Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Statistics Tags , , , ,

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. CS is a central problem in Statistics, Operations Research and Machine Learning which arises in applications such as signal processing, data compression, image reconstruction, and multi-label … Read more

Outlier detection in regression: conic quadratic formulations

Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , ,

In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic terms, each given by the product of a binary variable and a quadratic term of the continuous variables. Existing approaches in … Read more