5 research outputs found
Differential stability of convex optimization problems with possibly empty solution sets
As a complement to two recent papers by An and Yen [An, D.T.V., Yen, N.D.:
Differential stability of convex optimization problems under inclusion
constraints. Appl. Anal., 94, 108--128 (2015)], and by An and Yao [An, D.T.V.,
Yao, J.-C.: Further results on differential stability of convex optimization
problems. J. Optim. Theory Appl., 170, 28--42 (2016)] on subdifferentials of
the optimal value function of infinite-dimensional convex optimization
problems, this paper studies the differential stability of convex optimization
problems, where the solution set may be empty. By using a suitable sum rule for
-subdifferentials, we obtain exact formulas for computing the
-subdifferential of the optimal value function. Several
illustrative examples are also given
Subdifferential Stability Analysis for Convex Optimization Problems via Multiplier Sets
This paper discusses differential stability of convex programming problems in
Hausdorff locally convex topological vector spaces. Among other things, we
obtain formulas for computing or estimating the subdifferential and the
singular subdifferential of the optimal value function via suitable multiplier
sets
Differential Stability of Convex Discrete Optimal Control Problems
Differential stability of convex discrete optimal control problems in Banach
spaces is studied in this paper. By using some recent results of An and Yen
[Appl. Anal. 94, 108--128 (2015)] on differential stability of parametric
convex optimization problems under inclusion constraints, we obtain an upper
estimate for the subdifferential of the optimal value function of a parametric
convex discrete optimal control problem, where the objective function may be
nondifferentiable. If the objective function is differentiable, the obtained
upper estimate becomes an equality. It is shown that the singular
subdifferential of the just mentioned optimal value function always consists of
the origin of the dual space.Comment: accepted for publication in Acta Mathematica Vietnamic
Differential stability of a class of convex optimal control problems
A parametric constrained convex optimal control problem, where the initial
state is perturbed and the linear state equation contains a noise, is
considered in this paper. Formulas for computing the subdifferential and the
singular subdifferential of the optimal value function at a given parameter are
obtained by means of some recent results on differential stability in
mathematical programming. The computation procedures and illustrative examples
are presented
Subgradients of Marginal Functions in Parametric Control Problems of Partial Differential Equations
The paper studies generalized differentiability properties of the marginal
function of parametric optimal control problems of semilinear elliptic partial
differential equations. We establish upper estimates for the regular and the
limiting subgradients of the marginal function. With some additional
assumptions, we show that the solution map of the perturbed optimal control
problems has local upper H\"{o}lderian selections. This leads to a lower
estimate for the regular subdifferential of the marginal function