The quasidifferential descent method in a control problem with nonsmooth objective functional

Fominyh, Alexander

doi:10.1007/s11590-021-01710-7

Cited by 7 publications

(6 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us now prove inequality (29). By our assumption the function H 0 is strongly convex in (x, u) with modulus µ. Consequently, for a.e.…”

Section: And Correctness Of Stopping Criteriamentioning

confidence: 88%

See 1 more Smart Citation

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Долгополик¹

2023

Preprint

View full text Add to dashboard Cite

A class of exact penalty-type local search methods for optimal control problems with nonsmooth cost functional, nonsmooth (but continuous) dynamics, and nonsmooth state and control constraints is presented, in which the the penalty parameter and several line search parameters are adaptively adjusted during the optimisation process. This class of methods is applicable to problems having a known DC (Differenceof-Convex functions) structure and in its core is based on the classical DCA method, combined with the steering exact penalty rules for updating the penalty parameter and an adaptive nonmonotone line search procedure. Under the assumption that all auxiliary subproblems are solved only approximately (that is, with finite precision), we prove the correctness of the proposed family of methods and present its detailed convergence analysis. The performance of several different versions of the method is illustrated by means of a numerical example, in which the methods are applied to a semi-academic optimal control problem with a nonsmooth nonconvex state constraint.

show abstract

“…Let us now prove inequality (29). By our assumption the function H 0 is strongly convex in (x, u) with modulus µ. Consequently, for a.e.…”

Section: And Correctness Of Stopping Criteriamentioning

confidence: 88%

“…An approach to some nonsmooth optimal control problems based on smoothing approximations was considered by Noori Skandari et al [25,57]. Finally, the quasidifferential descent method for optimal control problems with nonsmooth objective functional was developed by Fominyh [29] (see also the references therein).…”

Section: Introductionmentioning

confidence: 99%

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Долгополик¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The order cancellation law or Rådström cancellation theorem [23,25], investigated also in [15,18,20], enables an embedding of a semigroup of convex sets into a quotient vector space called a Minkowski-Rådström-Hörmander space [12,28]. This space plays a crucial role in differentiation of nonsmooth functions (quasidifferential calculus of Demyanov and Rubinov [1,7,8,11,14,21]) and in integration and differentiation in the theory of multifunctions [5,6]. The cancellation by unbounded sets is especially challenging.…”

Section: Introductionmentioning

confidence: 99%

Order Cancellation Law in a Semigroup of Closed Convex Sets

Grzybowski¹,

Przybycień²

2022

Taiwanese J. Math.

View full text Add to dashboard Cite

In this paper we generalize Robinson's version of an order cancellation law in which some unbounded subsets of a vector space are cancellative elements. We introduce the notion of weakly narrow sets in normed spaces, study their properties and prove the order cancellation law where the canceled set is weakly narrow. Also, we prove the order cancellation law for closed convex subsets of topological vector space where the canceled set has bounded Hausdorff-like distance from its recession cone. We topologically embed the semigroup of closed convex sets sharing a recession cone having bounded Hausdorff-like distance from it into a topological vector space. This result extends Bielawski and Tabor's generalization of Rådström theorem.

show abstract

“…These methods were also applied to constructing optimal control in problems with the subdifferentiable quality functional in paper [19] and also to the problem of transferring a system of differential equations from one point to another in works [20], [21]. The finite-dimensional quasidifferential descent method was applied to optimization of a control system with a nonsmooth objective functional in Mayer form in paper [22]. Despite the fact that in the last works listed the quality functional is subdifferentiable, it has a special structure (for example, being the maximum of Gateaux differentiable functionals); therefore, the calculation of its subdifferential is quite simple.…”

Section: Introductionmentioning

confidence: 99%

The Subdifferential Descent Method in a Nonsmooth Variational Problem

Fominyh¹

2022

Preprint

View full text Add to dashboard Cite

The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to be subdifferentiable. Under some natural conditions the subdifferentiability of the functional considered is proved. The problem of finding the subdifferential descent is being solved and the subdifferential descent method is applied to solve the original problem. The algorithm developed is demonstrated by examples.

show abstract

The quasidifferential descent method in a control problem with nonsmooth objective functional

Cited by 7 publications

References 26 publications

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

An adaptive exact penalty method for nonsmooth optimal control problems with nonsmooth nonconvex state and control constraints

Order Cancellation Law in a Semigroup of Closed Convex Sets

The Subdifferential Descent Method in a Nonsmooth Variational Problem

Contact Info

Product

Resources

About