Nondifferentiable and quasidifferentiable duality in vector optimization theory
Nonessential objective functions in linear multiobjective optimization problems
Nonlinear conjugate gradient methods
Modifications of nonlinear conjugate gradient method are described and tested.
Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization.
Nonlinear Duality And Multiplier Theorems.
Nonlinear dynamic systems and optimal control problems on time scales
This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula...
Nonlinear dynamic systems and optimal control problems on time scales*
This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing L1-strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration by parts formula...
Nonlinear iterative methods and parallel computation
Nonlinear mixed zero-one Programming: Practical and Theoretical Aspects
Nonlinear multiple hybrid procedures for solving some constrained nonlinear optimization problems
We introduce a new formulation of multiple hybrid procedures which consist in a combination of k arbitrary approximate solutions. The connection between this method and other vector sequence transformations is studied. This connection is also exploited for solving some constrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.
Nonlinear nonconvex optimization by evolutionary algorithms applied to robust control.
Nonlinear optimization using the generalized reduced gradient method
Non-linear programming and the maximum principle for discrete time optimal control problems
Nonlinear Rescaling Method and Self-concordant Functions
Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is...
Nonlinear Successive Over-Relaxation.
Nonmonotone strategy for minimization of quadratics with simple constraints
An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified...
Non-monotoneous parallel iteration for solving convex feasibility problems
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm...
Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion
We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations , t=1,2,..., with i.i.d. -valued random vectors , which are observable but whose density ϱ is unknown.
Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application...
Nonparametric Maximum Likelihood Estimation of a Probability Density via Mathematical Programming.