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Second-order characterization of convex map**s in Banach spaces and its applications
We show that the positive semi-definiteness of the regular or limiting (Mordukhovich) second-order subdifferential of an approximately convex...
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A Second Order Primal–Dual Dynamical System for a Convex–Concave Bilinear Saddle Point Problem
The class of convex–concave bilinear saddle point problems encompasses many important convex optimization models arising in a wide array of...
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Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth...
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A Note on Generalized Second-Order Value Iteration in Markov Decision Processes
Value iteration is one of the first-order algorithms to approximate the solution of the Bellman equation arising from the Markov Decision Process...
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Convergence Results for a Class of Generalized Second-Order Evolutionary Variational–Hemivariational Inequalities
In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The...
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Generalized derivatives of optimal-value functions with parameterized convex programs embedded
This article proposes new practical methods for furnishing generalized derivative information of optimal-value functions with embedded parameterized...
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The Nonconvex Second-Order Cone: Algebraic Structure Toward Optimization
This paper explores the nonconvex second-order cone as a nonconvex conic extension of the known convex second-order cone in optimization, as well as...
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Generalized Subharmonic and Weakly Convex Functions
This paper is devoted to a conjecture formulated by Francesco Altomare and Ioan Raşa in 1999. It is concerned with the relationship between some...
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Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications
In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized...
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A Class of Analytic Functions Defined by a Second Order Differential Inequality and Error Function
In this article, we introduce and investigate a novel class of analytic functions that are defined through a second-order differential inequality in...
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Convex mixed-integer nonlinear programs derived from generalized disjunctive programming using cones
We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We...
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Generalization of Hermite-Hadamard Inequality for Twice Differentiable Convex and Quasi-Convex Functions
In this paper we obtain a new generalized integral identity involving a second-order differentiable function. The generalized Hermite-Hadamard...
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A Generalized Non-convex Method for Robust Tensor Completion
In this paper, we concentrate on the robust tensor completion (RTC) problem, which aims to recover a low-rank tensor from partial observations...
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Characterization of Convex and Generalized Convex Vector Fields on Riemannian Manifolds
In this paper, we define the concepts of C -convexity and generalized C -convexity of vector fields on Riemannian manifolds and we prove that a locally...
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Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints
This paper investigates nonsmooth multiobjective fractional programming (NMFP) with inequalities and equalities constraints in real reflexive Banach...
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On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built...
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Convex functions
Convex functions and convex sets are somewhat interdependent. When studying convex sets, some convex functions play a very important role (mainly the...
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The BVP of a class of second order linear fuzzy differential equations is solved by Green function method under the concept of granular differentiability
In the paper we use recently proposed concepts of granular derivative and horizontal membership function to introduce and study the equivalence...
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On generalized second-order proto-differentiability of the Benson proper perturbation maps in parametric vector optimization problems
This paper is concerned with second-order sensitivity analysis of parameterized vector optimization problems via generalized second-order contingent...