We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope an iterative algorithm which solves MIP relaxat...

Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...

In this paper recently developed mixed-integer programming (MIP) tools to the problem of optimal siting and sizing of distributed generators in a distribution network. Here three methodologies for solving the DGPP via mixed-integer linear programming (MILP) and mixed-integer nonlinear programming (MINLP) approaches are compared. The single MILP approach uses the well-known DC linear approximati...

In this study, a flexible optimization approach is introduced to design an optimal biocompatible solvent for an extractive fermentation process with cell-recycling. The optimal process/solvent design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objectives and the constraints. A flexible or fuzzy opti...

The problem of data reconciliation and the detection and identification of gross errors, such as measurement bias, are closely related and permits a solution within a mixed integer optimization framework. A mixed-integer linear programming (MILP) approach has been previously investigated by Soderstrom et al. (2001), where the process model was described by a set of linear equations. This paper ...

Université Paris-Dauphine LAMSADE Habilitation à diriger des Recherches Reformulations and Decompositions of Mixed Integer Linear and Nonlinear Programs

A conic integer program is an integer programming problem with conic constraints.Manyproblems infinance, engineering, statistical learning, andprobabilistic optimization aremodeled using conic constraints. Herewe studymixed-integer sets definedby second-order conic constraints.We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second...

A mixed-integer optimal control framework for analyzing the interaction of process synthesis, design, and control is presented in this paper. The approach integrates the economic design and dynamic controllability into a multiobjective Mixed-Integer Optimal Control Problem (MIOCP). The problem formulation includes dynamic models and incorporates both discrete and continuous decisions. An algori...

This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garver’s 6-bus...