A Monotonic Optimization Approach for Solving Strictly Quasiconvex Multiobjective Programming Problems

A Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for the non convex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM Journal on Optimization 15, 4, 953-970, 2005).

A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization

In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal parameters are bounded we prove the convergence of the sequence generated by the algorithm and when the objective functions are continuous, we prove the convergence to a generalized critical point. Furthermore, if each iteration minimize the proximal regularized function and the proximal parameters converges to zero we prove the convergence to a weak Pareto s…

非凸极小极大与多目标优化问题的非单调自适应步长最速梯度法

A Steepest Gradient Method with Nonmonotone Adaptive Step-sizes for the Nonconvex Minimax and Multi-Objective Optimization Problems

本文提出一种采用非单调自适应步长的新的最速梯度下降法，用于求解非凸极小极大问题，并将其扩展到多目标优化，证明了在拟凸和伪凸条件下的收敛性，数值实验验证了理论结果。

The inexact projected gradient method for quasiconvex vector optimization problems

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is important to have practical solution approaches for computing. In this work, we consider the inexact projected gradient-like method for solving smooth constrained vector optimization problems. Basically, we prove global convergence of any sequence produced by the method to a stationary point assuming that the objective function of the problem is $K$-quasiconv…

多目标分数双层优化问题的最优性条件与对偶性

Optimality Conditions and Duality for Multiobjective Fractional Bilevel Optimization Problems

本文提出了一种多目标分数双层优化问题的最优性条件与对偶性研究方法，利用非光滑约束资格条件和广义凸性概念，建立了更精细的最优性条件并证明了对偶定理。

一种求解无单调性拟凸均衡问题的外梯度算法

An extragradient algorithm for quasiconvex equilibrium problems without monotonicity

针对拟凸均衡问题，提出一种以法次梯度为搜索方向、自适应更新步长的外梯度算法，在无单调性和 Lipschitz 条件下证明其收敛到 ρ-拟解或精确解。