Related papers: On the Complexity of Inverse Mixed Integer Linear …
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
A constrained optimization problem is primal infeasible if its constraints cannot be satisfied, and dual infeasible if the constraints of its dual problem cannot be satisfied. We propose a novel iterative method, named proportional-integral…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…
This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order…
Inverse reinforcement learning (IRL) addresses the problem of recovering a task description given a demonstration of the optimal policy used to solve such a task. The optimal policy is usually provided by an expert or teacher, making IRL…
The irregular strip-packing problem consists of the computation of a non-overlapping placement of a set of polygons onto a rectangular strip of fixed width and the minimal length possible. Recent performance gains of the Mixed-Integer…
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…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
Mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…
The paper is concerned with a class of nonlinear free boundary problems, which are usually solved by variational methods based on primal (or primal-dual) variational settings. We deduce and investigate special relations (error identities).…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Arising from many applications at the intersection of decision making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) Problems unify the two main classes of inference, namely maximization (optimization) and marginal…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…