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Fixed point theorems in graphical cone metric spaces and application to a system of initial value problems
In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type...
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IPRSOCP: A Primal-Dual Interior-Point Relaxation Algorithm for Second-Order Cone Programming
Inspired by the smoothing barrier augmented Lagrangian function in Liu et al. (Math Methods Oper Res 96(3):351–382, 2022), we propose a primal-dual...
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Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming
Nonlinear symmetric cone programming (NSCP) generalizes important optimization problems such as nonlinear programming, nonlinear semi-definite...
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Fredholm integral equation in composed-cone metric spaces
The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples...
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The Homogenization Cone: Polar Cone and Projection
Let C be a closed convex subset of a real Hilbert space containing the origin, and assume that K is the homogenization cone of C , i.e., the smallest...
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Continuous controlled cone metric-type spaces over real Banach algebras and fixed-point results
In this article, we introduce a new geometrical structure that is the hybrid of a cone metric space over Banach algebra and a controlled metric-type...
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Approximation hierarchies for copositive cone over symmetric cone and their comparison
We first provide an inner-approximation hierarchy described by a sum-of-squares (SOS) constraint for the copositive (COP) cone over a general...
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Probability of Random Vector Hitting Truncated Polyhedral Cone: Majorization Aspect
AbstractThe paper presents conditions under which the probability of hitting a linear combination of random vectors in a compressed (from above)...
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A new corrector–predictor interior-point method for symmetric cone optimization
In this work, we present a corrector–predictor interior-point method for symmetric cone optimization based on Euclidean Jordan algebras as a key...
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Interior-point algorithm for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations
We generalize a primal-dual interior-point algorithm (IPA) proposed recently in (Illés T, Rigó PR, Török R Unified approach of primal-dual...
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Quasihyperbolic Geodesics are Cone Arcs
This paper focuses on the geometric properties of quasihyperbolic geodesics in centered John metric spaces. Our contribution is to provide a...
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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 Kannan-type contraction and fixed point theorems
In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying...
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A Novel Approach to Fixed Point Theorems in 2-Cone Normed Spaces over Banach Algebras
AbstractThe main goal of this paper is to establish a new approach for some existence and uniqueness of fixed points theorems in 2-cone normed space...
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Smooth and Discrete Cone-Nets
Cone-nets are conjugate nets on a surface such that along each individual curve of one family of parameter curves there is a cone in tangential...
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DC semidefinite programming and cone constrained DC optimization II: local search methods
The second part of our study is devoted to a detailed convergence analysis of two extensions of the well-known DCA method for solving DC (Difference...
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A Predictor-Corrector Algorithm for Semidefinite Programming that Uses the Factor Width Cone
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve...
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Common fixed point theorems on quasi-cone metric space over a divisible Banach algebra
In this manuscript, we investigate the existence and uniqueness of a common fixed point for the self-map**s defined on quasi-cone metric space over...
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Cone 3-Manifolds
This is an overview on hyperbolic cone 3-manifolds, their deformation theory and their role in Thurston’s orbifold theorem. We also describe the...
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