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Best Möbius Approximations of Convex and Concave Map**s
We study the best Möbius approximations (BMA) to convex and concave conformal map**s of the disk, including the special case of map**s onto...
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Robust Bond Portfolio Construction via Convex–Concave Saddle Point Optimization
The minimum (worst case) value of a long-only portfolio of bonds, over a convex set of yield curves and spreads, can be estimated by its...
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An accelerated minimax algorithm for convex-concave saddle point problems with nonsmooth coupling function
In this work we aim to solve a convex-concave saddle point problem, where the convex-concave coupling function is smooth in one variable and...
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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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Improved Convex and Concave Relaxations of Composite Bilinear Forms
Deterministic nonconvex optimization solvers generate convex relaxations of nonconvex functions by making use of underlying factorable...
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Multiple Solutions for Discrete Schrödinger Equations with Concave–Convex Nonlinearities
In the present paper, we study a class of discrete Schrödinger equations with concave–convex nonlinear terms via the variational method. Under...
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Convex envelopes for ray-concave functions
Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization...
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A unified single-loop alternating gradient projection algorithm for nonconvex–concave and convex–nonconcave minimax problems
Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence...
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Convex and concave envelopes of artificial neural network activation functions for deterministic global optimization
In this work, we present general methods to construct convex/concave relaxations of the activation functions that are commonly chosen for artificial...
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Double phase systems with convex–concave nonlinearity on complete manifold
This study investigates the double-phase system with infinite potentials that vanish and convex–concave nonlinearity in Sobolev spaces with variable...
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Fractional Musielak spaces: a class of non-local problem involving concave–convex nonlinearity
In this research, we analyze the existence and multiplicity of nonnegative solutions for a class of non-local elliptic problems with Dirichlet...
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Efficient Convex Optimization for Non-convex Non-smooth Image Restoration
This work focuses on recovering images from various forms of corruption, for which a challenging non-smooth, non-convex optimization model is...
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A new computational framework for log-concave density estimation
In statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great...
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Infinitely many solutions for quasilinear Schrödinger equation with concave-convex nonlinearities
In this work, we study the existence of infinitely many solutions to the following quasilinear Schrödinger equations with a parameter α and a...
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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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Optimization of the Optimal Value Function in Problems of Convex Parametric Programming
We consider a problem of convex parametric programming in which the objective function and the constraint functions are convex functions of an...
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The Multiplicity of Nonnegative Nontrivial Solutions for p(x)-Kirchhoff Equation with Concave–Convex Nonlinearities
This paper is devoted to study a class of p ( x )-Kirchhoff equation with concave–convex nonlinearities. By means of perturbation technique and the...
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