Related papers: A Note on the Paper "Optimality Conditions for Vec…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
In this paper, we continue to study pairwise ($k$-semi-)stratifiable bitopological spaces. Some new characterizations of pairwise $k$-semi-stratifiable bitopological spaces are provided. Relationships between pairwise stratifiable and…
We provide a new and significantly shorter optimality proof of recent quantified Tauberian theorems, both in the setting of vector-valued functions and of $C_0$-semigroups, and in fact our results are also more general than those currently…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…
The recent results of An, Luan, and Yen [Differential stability in convex optimization via generalized polyhedrality. Vietnam J. Math. https://-doi.org/10.1007/s10013-024-00721-y] on differential stability of parametric optimization…
This article revisits previous results presented in Optimization which were challenged later by Voisei and Zalinescu (V-Z) in the same journal. We aim to use the points of view of V-Z to modify the original results and highlight that the…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
We obtain existence and convergence theorems on two variants of the proximal point algorithm for proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.
This paper deals with $\varepsilon$-efficient and $\varepsilon$-properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the paper, we establish a new nonlinear separation theorem for…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
We give a sketch for an alternative proof of a recent result by J. Tseng.
This paper is devoted to present two counterexamples to the theorem from \cite{MK} Maria R., Katherine T. M., Bernardo S. M., Extremal graphs with bounded vertex bipartiteness number, Linear Algebra Appl. 493 (2016) 28-36. Moreover, the…
This note concerns the paper by Benslimane et Gadhi (JMAA. doi: 10.1016/j.jmaa.2023.127117) where the authors established necessary optimality conditions for an optimization problem (P) governed by a double phase partial di{\S}erential…
In this paper, we give sufficient conditions on the spectral radius for a bipartite graph to Hamiltonian and traceable, which expand the results of Lu, Liu and Tian (2012) [10]. Furthermore, we also present tight sufficient conditions on…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
In this paper, we present some second-order sufficient conditions in terms of the Demyanov-Pevnyi's second-order directional derivatives for efficiency of $C^1$ vector optimization problems with constraints. Our results improve and…
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples…
We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…