Extendability of continuous quasiconvex functions from subspaces
, 2022 Let $Y$ be a subspace of a topological vector space $X$, and $A\subset X$ an open convex set that intersects $Y$. We say that the property $(QE)$ [property $(CE)$] holds if every continuous quasiconvex [continuous convex] function on $A\cap Y$ admits a ...
Veselý, Libor +1 more
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Energy-Efficient Trajectory Optimization for UAV-Based Hybrid FSO/RF Communications with Buffer Constraints. [PDF]
Entropy (Basel), 2021 Lu RR +5 more
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Quasiconvex relaxations based on interval arithmetic
, 2001 Interval analysis provides a tool for (i) forward error analysis, (ii) estimating and controlling rounding and approximation errors automatically, and (iii) proving existence and uniqueness of solutions. In this context the terms self-validating methods,
Jansson, Christian, Christian Jansson
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Full convergence of the proximal point method for quasiconvex functions on Hadamard manifolds [PDF]
, 2011 In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on Hadamard manifolds. To reach this goal, we initially extend the concepts of regular and generalized subgradient from
Erik A. Papa Quiroz +3 more
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About the kernel of the strongly quasiconvex function generated projection [PDF]
This paper explores a natural generalization of Euclidean projection through the lens of strongly quasiconvex functions, as developed in prior works. By establishing a connection between strongly quasiconvex functions and the theory of mutually polar ...
Németh, S. Z., Németh, A. B.
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Least Squares Estimation of a Quasiconvex Regression Function
, 2023 We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares estimator (LSE) and ...
Mukherjee, Somabha +3 more
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Horizontally quasiconvex envelope in the Heisenberg group [PDF]
This paper is concerned with a PDE-based approach to the horizontally quasiconvex (h-quasiconvex, for short) envelope of a given continuous function in the Heisenberg group.We provide a characterization for upper semicontinuous, h-quasiconvex functions ...
Zhou, Xiaodan +2 more
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On the Hessian matrix and Minkowski addition of quasiconvex functions
, 2007 We study the class Q of quasiconvex functions (i.e. functions with convex sublevel sets), by associating to every u∈Q∩C(Rn) a function H:Rn×R→R∪{±∞}, such that H(X,t) is nondecreasing in t and sublinear in X: for every fixed t, the function H(⋅,t) is ...
Salani, Paolo, Longinetti, Marco
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Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations. [PDF]
Comput Methods Appl Mech Eng, 2022 Tac V, Sahli Costabal F, Tepole AB.
europepmc +1 more source
On strong quasiconvexity of functions in infinite dimensions
Optimization LettersIn this paper, we explore the concept of $σ$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by analyzing certain operations on functions that preserve $σ$-quasiconvexity.
Nam, Nguyen Mau, Sharkansky, Jacob
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