Related papers: On the complexity of nonlinear mixed-integer optim…
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the…
We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data…
In this paper, we design $MC^2$ algorithms for Mixed Integer and Linear Programming. By expressing a constrained optimisation as one of simulation from a Boltzmann distribution, we reformulate integer and linear programming as Monte Carlo…
Gamma uncertainty sets have been introduced for adjusting the degree of conservatism of robust counterparts of (discrete) linear programs. The contribution of this paper is a generalization of this approach to (mixed integer) nonlinear…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…
Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot…
Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
We study the integrality gap of convex mixed-integer programs, that is, the difference between the optimal value of such a problem and the optimal value of its continuous relaxation. We study classes of convex sets whose associated…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…