Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to study ...

A novel Polak-Ribière-Polyak (PRP) type conjugate gradient method is proposed to solve a nonconvex vector optimization. This variant is a nontrivial extension of a PRP type conjugate gradient method from the scalar case to the vector case. We ...

This paper explores the potential of (nonlinear) conic constraints to tighten the relaxations of spatial branch-and-bound algorithms. More precisely, we contribute to the literature on the use of conic optimization for the efficient solution, to ...$\mathrm{}$

In this paper, we introduce a new shape functional defined for toroidal domains that we call harmonic helicity, and study its shape optimization. Given a toroidal domain, we consider its associated harmonic field. The latter is the magnetic field ...${}^{\mathrm{}}$

In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitz operator, a cocoercive operator, and a linear composite term. In the ...

To ensure the system stability of the ${\mathcal{H}}_2$-guaranteed cost optimal decentralized control (ODC) problem, we formulate an approximate semidefinite programming (SDP) problem that leverages the block diagonal structure of the decentralized controller’s ...${\mathcal{}}_{\mathrm{}}$

This paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the intensive care unit (ICU) capacity. The vaccination ...$\mathrm{}$

We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact formula for the Clarke subdifferential of the probability function ...

This paper considers the decentralized online strongly convex optimization over a multi-agent network, where the objective is to minimize a global loss function accumulated by the local loss functions of all agents. The Time-Varying Scaling ...

We show that projected solutions of a generalized game correspond to classical ones of an auxiliary generalized game obtained by doubling the number of players. Based on this reformulation and using known results for the existence of classical ...

In this paper, we investigate continuity properties of the efficient solution map of a parametric nonlinear multiobjective optimal control problem. First, by using the equimeasurability condition of the admissible control set, we obtain the ...

This paper focuses on analyzing the boundness of the solution set for the vertical tensor complementarity problem (VTCP). We introduce two novel quantities related to tensor sets, establish the interconnections between these introduced quantities, ...${}_{\mathrm{}}$${}_{\mathrm{}}$${}_{\mathrm{}}$

Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy ...

In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives (which are also called Mordukhovich coderivatives) for the metric projection ...

This paper mainly studies the existence of $\alpha$-robust weak Nash equilibria for leader-follower population games with fuzzy parameters. First, $\alpha$-robust weak Nash equilibria for population games with fuzzy parameters are defined based on u-type set ...

The authors study the twice codifferentiable functions introduced by Professor V.F. Demyanov and how to calculate their second codifferentials. We proved that a twice hypodifferentiable positively homogeneous (p.h.) function of the second order is ...

In this paper, we study the standard formulation of an optimization problem when the computation of gradient is not available. Such a problem can be classified as a “black box” optimization problem, since the oracle returns only the value of the ...

We propose a distributed optimization method based on a unified momentum method combined with the heavy ball method and optimized gradient method. We first prove that the stochastic version of the unified momentum method converges, and then prove ...

In this paper, we introduce a modulus-based formulation for solving vertical tensor complementarity problems (VTCP) with an arbitrary number of tensors. This formulation allows us to design the modulus-based tensor splitting iterative method to ...