联合凸函数是指具有凸性质的多元函数，它的定义域是一个凸集合，且对于任意两个点的线性组合，函数值都小于等于这两个点在函数上的线性组合。这种函数具有一些重要的性质，比如局部最小值就是全局最小值。联合凹函数是指具有凹性质的多元函数，它的定义域是一个凹集合，且对于任意两个点的线性组合，函...
A. Dreves and J. Gwinner. Jointly convex generalized Nash equilibria and ellip- tic multiobjective optimal control. J. Optim. Theory Appl., 168(3):1065-1086, 2016. doi: 10.1007/s10957-015-0788-7.A. Dreves and J. Gwinner. Jointly convex generalized Nash equilibria and elliptic multi...
Hence, the loss function is biconvex. Instead of using a generic optimizer, we exploited the biconvex nature of this problem and effectively optimized the function by using alternative convex search, which iteratively updates these two variables31. Algorithm 1. sigLASSO algorithm 1: initialization:...
For fully observed and partially observed systems, we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists, provided that the quantizers allowed are ones which have convex codecells. Furthermore, optimal control policies are linear in...
If Q(xL) > 0 and Q(xH) < 0, then a sufficient condition that Q(x) is unimodal is that: 1) q(x) is positive, increasing, and (weakly) concave, where 0 < q(x) < 1; and 2) c(x) is positive, increasing, and (weakly) convex, where \( 0<c(x)<\frac...
It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently [4] .doi:10.1016/j.laa.2018.03.002Virosztek...
In the considered problems, the switching communication networks are supposed to be jointly strongly connected, and each player’s action set is supposed to be compact and convex. By utilizing the projected gradient play and the consensus protocol, distributed Nash equilibrium seeking strategies are ...
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We investigate refinements of an existing nonconvex programming algorithm that exploits special structure of linear complementarity problems. We construct a linear program, having an n × n working basis, which is equivalent to the subproblems generated by the algorithm that generally require 3n × 3n...
The convex curve in the contacting surface 20 is intersected by a concave curve 21, the juncture forming a substantially fitting edge 22, which is free to move over the abutting concave surface 23, while at all times the two concurrent concave surfaces jointly comprise a smoothly curved ...