A new algorithm for the optimization of nonlinear systems under uncertainty is presented. The algorithm, based on a parametric programming framework, gives a complete map of the optimal solution in the space of the uncertain parameters, solving a minimum number of NLP subproblems and simplified multiparametric linear master problems. Through cumulative outer-approximations obtained from the sol...

This research presents an efficient energy management system (EMS) for battery storage systems (BESS) connected to monopolar DC distribution networks which considers a high penetration of photovoltaic generation. The optimization model that expresses the EMS with BESS and renewable generation can be classified as nonlinear programming (NLP) model. study reformulates NLP recursive convex approxi...

This paper presents an approximate multi-parametric Nonlinear Programming (mp-NLP) approach to explicit solution of feedback min-max NMPC problems for constrained nonlinear systems in the presence of bounded disturbances and/or parameter uncertainties. It is based on an orthogonal search tree structure of the state space partition and consists in constructing a piecewise nonlinear (PWNL) approx...

A branch and cut algorithm is developed for solving 0-1 MINLP problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions Nonlinear Programming (NLP) problems are solved, using a primal-dual interior point algorithm. The objective and constraints ar...

• Dynamic performance under various forms of disturbances. Nonlinear programming formulation for dispatch virtual inertia and damping. Semi-definite relaxation to address non-convexity. Clique decomposition approach exploit sparsity. Distributed solution based on the alternating direction method multipliers. Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual ...

In the article, we present an efficient optimization framework that solves trajectory problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier subproblems. With fixed, can be optimized efficiently using convex optimization, and in separate NLP, which forms bilevel problem. The challenge of obtaining gradi...

This article presents the formulation and the solution of a class of Mixed-integer Nonlinear Programming (MINLP) problems, applied to optimal synthesis of process systems in a modular simulator environment. The proposed algorithm makes use of module, reduces the work of calculation on model equations, makes the size of MINLP smaller. The algorithm consists of solving alternate sequences of MILP...

Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadra...

Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial productio...