5.2 Modeling with the exponential cone 利用指数锥扩展圆锥优化工具箱,可以获得新类型的约束构件和新类型的可表示集合。本节将列出指数锥的基本操作。 5.2.1 Exponential 上镜图(epigraph)t≥ex是Kexp的一个部分: 5.2.2 Logarithm 同样,我们也可以表示下镜图t≤logx,x≥0: ...
5 Exponential cone optimization¶So far we discussed optimization problems involving the major “polynomial” families of cones: linear, quadratic and power cones. In this chapter we introduce a single new object, namely the three-dimensional exponential cone, together with examples and applications....
Exponential-cone optimizationInterior-point methodsA new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It is a generalization of the famous algorithm suggested by Nesterov and Todd for the symmetric conic case, and uses primal-dual scalings for ...
Entry Trajectory Optimization by Second-Order Cone Programming Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming. This paper represents an attempt ... ...
We first characterize the nonemptiness and compactness of the weakly efficient solution set of a cone-constrained convex vector optimization problem in a finite-dimensional space when the objective space is ordered by some nontrivial polyhedral cone,and apply the characterizations to the convergence anal...
A novel generalized oppositional biogeography-based optimization algorithm: application to peak to average power ratio reduction in OFDM systems Special Issue on Recent Developments in Differential Equations Modeling of vibration for functionally graded beams Special Issue on Recent Developments in Differen...
Minimize the CVaR : We solve the one-dimensional optimization problem (15)z∗∈argminz∈Rf(z). To conclude, we observe that the strategy (V0∗(z∗),ξ∗(z∗)) is the optimal one: min(V0,ξ)∈AṼ0CVaRa(L(V0,ξ))=CVaRa(L(V0∗(z∗),ξ∗(z∗))). 3. ...
In this paper, we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a single univariate root-finding problem. This leads to a fast ...
This paper introduces a method of solving dual constraints: to find the gain of the Full State Feed-back Controller (FSFC) using the cone complimentary linearization technique, along with the rate of decay of the NCS, thus assuring exponential stability of the same. The w...
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