Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond to systems involving partly smooth operators, and particular variational inequalities over sets. As classical nonlinear programming, such active‐set structure underlies the design of accelerated local Newton type. We formalize this idea b...

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We prove that some multivariate linear tensor product problems are tractable in the worst case setting if they are defined as tensor products of univariate problems with logarithmically increasing smoothness. This is demonstrated for the approximation problem defined over Korobov spaces and for the approximation problem of certain diagonal operators. For these two problems we show necessary and...

This paper presents a multi-objective Particle Swarm Optimization (PSO) algorithm for worker assignment and mixed-model assembly line balancing problem when task times depend on the worker’s skill level. The objectives of this model are minimization of the number of stations (equivalent to the maximization of the weighted line efficiency), minimization of the weighted smoothness index and minim...

‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...

for all x ∈ X, whereX denotes the dual space ofX and ⟨⋅, ⋅⟩ the generalized duality pairing between X and X. If X = H is a Hilbert space, then J becomes the identitymapping onH. A point x ∈ C is a fixed point of T : C ⊂ X → X provided Tx = x. Denote by F(T) the set of fixed points of T; that is, F(T) = {x ∈ C : Tx = x}. Let X be a normed linear space with dim X ≥ 2. The modulus of smoothness of...

Let f 2 C 1 ?1; 1] change its convexity nitely many times in the interval, say s times, at Y s : ?1 < y s < < y 1 < 1. We estimate the degree of simultaneous approximation of f and its derivative by polynomials of degree n, which change convexity exactly at the points Y s , and their derivatives. We show that provided n is suuciently large, depending on the location of the points Y s , the rate...