QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.

NONCOMPACT INFINITE OPTIMIZATION AND EQUILIBRIA OF CONSTRAINED GAMES IN GENERALIZED CONVEX SPACES

By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are proved in generalized convex spaces without linear structure. These theorems improve and generalize a number of important results in recent literature.

A new primal-dual path-following interior-point algorithm for linearly constrained convex optimization

In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).

An accelerated augmented Lagrangian method for linearly constrained convex programming with the rate of convergence O(1/k^2)

In this paper, we propose and analyze an accelerated augmented Lagrangian method（denoted by AALM） for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O（1/k^2） while the convergence rate of the classical augmented Lagrangian method（ALM） is O1 k. Numerical experiments on the linearly constrained 1-2minimization problem are presented to demonstrate the effectiveness of AALM.

Predictor-corrector interior-point algorithm for linearly constrained convex programming

Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.

CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY CONVEX H-SPACES

A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.

A POTENTIAL REDUCTION ALGORITHM FOR LINEARLY CONSTRAINED CONVEX PROGRAMMING

A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.

Levy Constrained Search in Fock Space：An Alternative Approach to Noninteger Electron Number

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

An Efficient Random Algorithm for Box Constrained Weighted Maximin Dispersion Problem

The box-constrained weighted maximin dispersion problem is to find a point in an n-dimensional box such that the minimum of the weighted Euclidean distance from given m points is maximized. In this paper, we first reformulate the maximin dispersion problem as a non-convex quadratically constrained quadratic programming (QCQP) problem. We adopt the successive convex approximation (SCA) algorithm to solve the problem. Numerical results show that the proposed algorithm is efficient.

融合边事件触发机制的分布式在线约束凸优化

现有分布式在线优化方法的实现通常依赖于通信网络中节点间的实时信息交换,这在实际应用中会带来无法承受的通信带宽等资源的消耗。为了减少通信成本,将边事件触发技术应用于分布式在线约束凸优化,其中每个智能体仅知晓时变的局部目标函数,所有智能体的公共目标是求解优化解序列来最小化网络总目标值(所有局部目标函数的总和)。首先,针对分布式在线梯度下降算法,在固定强连通有向图的假设下,设计了一个边事件触发机制。然后,基于所设计的边事件触发机制,为每个智能体的Regret建立了一个上界,发现该上界与事件触发阈值直接相关。进一步的分析表明,只要边事件触发阈值随着时间趋于无穷大而收敛至零时,Regret是次线性增长的。最后,通过面向时变经济调度和糖尿病分类预测问题的数值仿真实验,验证了所提出算法的有效性。

基于深度强化学习的联合通信感知系统波束优化方法

在不远的未来,ISAC系统将同时提供通信和感知服务。ISAC系统需要通过先进的波束优化算法保证所提供服务的质量,并满足形式多样的服务目标和资源约束。通常,波束算法可建模为一个优化问题。然而,基于传统优化理论设计的优化算法仅能处理带有瞬时约束的资源分配问题,而不能处理带有长时间约束的优化问题,从而降低了系统性能。一种可行的解决方案是基于RL理论设计相应算法来解决上述问题。然而,现有的工作主要致力于解决无约束RL问题,对约束强化学习问题关注较少,这限制了强化学习在波束优化问题中的应用。为了克服上述挑战,提出了一种基于CSSCA的RL方法。该方法将原有的目标函数和约束函数替换为对应的凸近似函数,通过求解一系列的凸近似问题,最终可以保证收敛到原问题的KKT点。最后,通过仿真结果展示了所提出方法的优越性。

凸约束方程组的新型无导数算法及在信号重构中的应用

提出一种新型无导数算法,以解决凸约束非线性方程组问题.该算法利用改进的共轭参数设计搜索方向,以确保算法的充分下降性和信赖域特性.在适当的假设下,该算法具有全局收敛性.数值仿真结果表明,该算法在处理凸约束非线性方程组问题和信号重构问题时具有高效性和鲁棒性.

非线性方程组的方向重启改进型算法及应用

提出一种方向重启改进的共轭梯度算法,旨在优化凸约束非线性方程组和稀疏信号恢复问题的求解过程。通过修正经典的共轭参数设计新的搜索方向,并结合投影技术与无导数线搜索技术来更新迭代点。新的搜索方向在不依赖于任何线搜索下具备充分下降性与信赖域特征,且在合理的假设下证明了新算法的全局收敛性质。数值实验结果表明,新算法在求解凸约束非线性方程组和信号恢复的应用场景中,相比同类算法具有更优的性能和更广泛的应用潜力。

广义共轭框架下约束复合优化的逆对偶

在可分离局部凸拓扑空间上,主要研究目标函数带有连续线性映射复合的约束优化问题.借助c-共轭模式和扰动法,得到了该约束复合优化的3个对偶问题,并且结合扰动函数的均匀凸性,具体给出了逆对偶成立的充分条件.

CONVERGENCE PROPERTIES OF PROJECTED GRADIENT METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR CONVEX CONSTRAINED OPTIMIZATION

This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature. A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.

单天线功率约束和统计CSI下的MU-MIMO下行链路线性预编码

近年来,多用户多输入多输出(Multiple-User Multiple-Input Multiple-Output,MU-MIMO)下行链路的预编码算法设计吸引了越来越多研究者的兴趣。然而目前并没有对基站端已知信道误差概率分布且约束条件为单天线功率约束(Per-Antenna Power Constraints,PAPCS)的情况下的线性预编码算法的研究。针对上述情况,以遍历和速率(Expected Sum Rate)最大化为优化准则,主要基于约束随机逐次凸近似(Constrained Stochastic Successive Convex Approximation,CSSCA)、二阶对偶法、交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)及高斯随机化(Gaussian Randomization)设计了线性预编码算法。所提算法的适用场景更符合实际情况,而且实验仿真结果证明,算法的性能较好。

一类纳什均衡问题的求解算法

随着纳什均衡问题被应用到多个领域,其求解算法也得到了越来越多的关注。但鉴于纳什均衡是由一系列优化问题组成的复杂系统,经典的约束优化算法不能被直接应用于求解该问题中,导致求解该问题的困难。对于一类效用函数是强凸的纳什均衡问题,利用Nikaido-Isoda函数将其转化为一类与之完全等价的光滑约束优化问题进行求解是一种有效途径。本文在纳什均衡问题效用函数的梯度具有强单调性这一假设条件下给出求解此类问题的Nikaido-Isoda算法并证明该算法具有全局收敛性。最后,通过求解两类经典纳什均衡问题,验证了该算法的可行性和有效性。

曲线设计中形状控制和能量控制的一种方法

插值曲线的形状控制和应变能的控制可部分地通过对插值函数的二阶导数的控制来实现．通过对分母为线性的有理三次插值样条的二阶导数的控制，将插值曲线的凸性控制和应变能的控制结合起来，给出了将插值函数的二阶导数约束于给定区间的算法及其实现条件．

具有性能约束几何布局优化模型的研究

建立了带性能约束圆域内几何布局优化问题的各种数学模型，其中图元 可为圆形、三角形及任意连通的二维几何图形。通过引入模函数与广义距离 函数等概念，详细论述了此类几何布局问题可转化为含有Ｄ．Ｃ．约束的凸规 划问题，从而为进一步研究几何布局优化问题的最优性条件、优化算法等奠 定了数学基础。

约束四面体剖分和三维物体表面重建

该文提出了约束曲面和约束最大空球凸多面体的概念,在此基础上设计了一种在空间区域上做约束Delaunay四面体剖分的算法。该算法的基本思路是首先对空间区域进行约束最大空球凸多面体剖分,然后在各个约束最大空球凸多面体内部做Delaunay四面体剖分。利用约束Delaunay四面体剖分算法,该文进一步设计了一种三维物体表面重建算法。