Related papers: Nonconvex piecewise linear functions: Advanced for…

The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is…

We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems we introduce the new concept of core points, i.e., integral points whose orbit polytopes are…

Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online…

Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…

In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions $\pi$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

This paper contributes to the theory of cutting planes for mixed integer linear programs (MILPs). Minimal valid inequalities are well understood for a relaxation of an MILP in tableau form where all the nonbasic variables are continuous;…

Accurate structural relaxation is critical for advanced materials design. Traditional approaches built on physics-derived first-principles calculations are computationally expensive, motivating the creation of machine-learning interatomic…

In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…

Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this…

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…

Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…

This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…

We present new models of optimization-based task and motion planning (TAMP) for robotic pick-and-place (P&P), which plan action sequences and motion trajectory with low computational costs. We improved an existing state-of-the-art TAMP…

We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…

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…

We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic Programming (MICP)…