We presented a separation based optimization algorithm which, rather than optimization the entire variables altogether, This would allow us to employ: 1) a class of nonlinear functions with three variables and 2) a convex quadratic multivariable polynomial, for minimization of reprojection error. Neglecting the inversion required to minimize the nonlinear functions, in this paper we demonstrate...

We discuss a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems appear in many applications and are of a different nature than systems of equations. Our approach uses an optimization-based multigrid algorithm in which the multigrid algorithm relies explicitly on nonlinear optimization models as subproblems on coarser grids. Our goal ...

Combustion optimization adjustment can effectively suppress NOx emissions from power plant boilers. Current combustion optimization adjustment methods involve nonlinear optimization based on the boiler combustion model, such as optimization by a genetic algorithm or particle swarm algorithm. The computational complexity of these methods results in poor real-time performance, which limits their ...

Constrained optimization problems have a wide range of applications in science, economics, and engineering. In this paper, a neural network model is proposed to solve a class of nonsmooth constrained optimization problems with a nonsmooth convex objective function subject to nonlinear inequality and affine equality constraints. It is a one-layer non-penalty recurrent neural network based on the...

In this overview paper, we first survey numerical approaches to solve nonlinear optimal control problems, and second, we present our most recent algorithmic developments for real-time optimization in nonlinear model predictive control. In the survey part, we discuss three direct optimal control approaches in detail: (i) single shooting, (ii) collocation, and (iii) multiple shooting, and we spec...

Nonlinear optimization algorithms are rarely discussed from a complexity point of view. Even the concept of solving nonlinear problems on digital computers is not well defined. The focus here is on a complexity approach for designing and analyzing algorithms for nonlinear optimization problems providing optimal solutions with prespecified accuracy in the solution space. We delineate the complex...

An algorithm is presented for solving nonlinear optimization problems with chance 5 constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at 6 least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained 7 nonlinear optimization problems that arise in sample average approximations of chance-constrained 8 ...

Induration furnaces for iron-oxide pellets are expensive processes, due to their high energy consumption. Moreover, they are highly interactive and then complex to control. Real-time optimization strategies based on reliable process models are thus necessary. However, induration furnaces are described by distributed-parameter models that require long computation times. The performance of IMCopt...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...