Multilocal programming aims to identify all local minimizers of unconstrained or constrained nonlinear optimization problems. The multilocal programming theory relies on global optimization strategies combined with simple ideas that are inspired in deflection or stretching techniques to avoid convergence to the already detected local minimizers. The most used methods to solve this type of probl...

In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time...

We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : :; m: SQP methods require the use of an auxiliary function, called a merit function or line-search function, for assessing the steps that are generated. We derive a merit function by adding slack variables to create ...

We deal with differential conditions for local optimality. The conditions we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based only on first and second order derivatives. A similar result is proved for equality constrained problems, although necessary conditions require regularity of the equality constraints.

This paper presents a problem-independent framework that uni es various mechanisms for solving discrete constrained nonlinear programming (NLP) problems whose functions are not necessarily di erentiable and continuous. The framework is based on the rst-order necessary and su cient conditions in the theory of discrete constrained optimization using Lagrange multipliers. It implements the search ...

Uncertainties may have a large impact on equipment decisions, plant operability, and economic analysis. Thus the consideration of uncertainties in optimization approaches is necessary for robust process design and operation. As a part of it, efficient chance constrained programming has become an important field of research in process systems engineering. In this work, a new approach is proposed...

A novel chance constrained programming approach for process optimization of large-scale nonlinear dynamic systems and control under uncertainty is proposed. The stochastic property of the uncertainties is explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. This incorporates the issue of feasibility and...

For some kinds of linearly constrained optimization problems with unique optimal solution, such as linear and convex problems, the single local optimum is also global. However, there are a broad variety of problems in which the property of unique solution cannot be simply postulated or verified. The paper presents an effective approach for the global linearly constrained optimization problem wi...