思路: 通过变量代换将nonconvex problem转化为convex problem。这个例子说明(non)convexity是coordinate depen...
Conditioning convex and nonconvex problems, J. Optim. Theory Appl. 90 (1996), no. 3, 535-554.Penot, J.-P.: Conditioning convex and nonconvex problems. J. Optim. Theor. Appl. 90 (3), 539–558 (1995) MathSciNetJ.-P. Penot, Conditioning convex and nonconvex problems, Journal of ...
大家或许不知道，（混合）整数规划被称为极度非凸问题（highly nonconvex problem），如下图：实心黑点组...
If the point x is degenerate andλ∈IRm+ satis,es (9), then x is the solution of the convex programming problem: Minimize,i∈I(x) (λi)gi(x),z−x, subject to z∈Ω. 4Since,i∈I(x)λi>0 we obtain that {z∈Ω| ,,gi(x),z−x,<0 for all i∈I(x)}=∅. ...
Adaptive Strategies in Non-convex Optimization An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competi... Z Zhuang 被引量: 0发表: 2023年 Communication-Efficient Distributed Blockwise Momentum ...
Recently, such an algorithm GradOpt based on GOA is proposed with amazing theoretical and experimental results, but it mainly studies the problem which consists of one nonconvex part. This paper aims to find the global solution of a nonconvex objective with a convex part plus a nonconvex part...
The simultaneous size and shape optimization of truss structures can represent the non-convex problems. In this paper, an improved particle swarm optimization algorithm is developed and applied to find global optimum solutions. The optimisation problem is concerned with minimizing the structural weight su...
Abstract In this survey paper we discuss recent developments in the turnpike theory for nonconvex (nonconcave) problems. We also establish a new result on agreeable solutions for variational problems with extended-valued integrands. JEL Classification:C6, O4 ...
(1.1) whereA k ∈R M×N k andq∈R M ;X k ⊂R N k isaclosedconvexset;(·)isasmooth (possiblynonconvex)function;andeachg k (·)canbeeitherasmoothfunctionor aconvexnonsmoothfunction.LetusdefineA:=[A 1 ,...,A k ].Theaugmented Lagrangianforproblem(1.1)isgivenby L(x;y)= K k...
OPTIMALITY CONDITIONS FOR NONCONVEX BILEVEL PROGRAMMING PROBLEMS An optimal control problem with a nonlinear control system embedded is considered. Using the endpoint map of the control system, such problems can be writt... LIU,Guoshan,HAN,... - 《Systems Science & Mathematical Sciences》 被引量...