Titlebook: Numerical Nonsmooth Optimization; State of the Art Alg Adil M. Bagirov,Manlio Gaudioso,Sona Taheri Book 2020 Springer Nature Switzerland AG

Palpitation

Local Search for Nonsmooth DC Optimization with DC Equality and Inequality Constraintshe cluster point of the sequence is the KKT point for the original problem with the Lagrange multipliers provided by an auxiliary linearized problem. Finally, on the base of the developed theory several new stopping criteria are elaborated, which allow to transform the local search scheme into a local search algorithm.

眉毛

Beyond the Oracle: Opportunities of Piecewise Differentiationdescribe the calculation of directionally active generalized gradients, generalized .-gradients and the checking of first and second order optimality conditions. All this is based on the abs-linearization of a piecewise smooth objective in abs-normal form.

食道

TEM

名字

Bundle Methods for Nonsmooth DC Optimizationhed. Bundle methods are developed based on a nonconvex piecewise linear model of the objective function and the convergence of these methods is studied. Numerical results are presented to demonstrate the performance of the methods.

Arctic

On Mixed Integer Nonsmooth Optimizationby using Clarke subgradients as a substitute for the classical gradient. Ideas for convergence proofs are given as well as references where the details can be found. We also consider how some algorithms can be modified in order to solve nonconvex problems including ..-pseudoconvex functions or even ..-quasiconvex constraints.

ALE

招募

Advances in Low-Memory Subgradient Optimization to execute these algorithms. To provide historical perspective this survey starts with the original result of Shor which opened this field with the application to the classical transportation problem. The theoretical complexity bounds for smooth and nonsmooth convex and quasiconvex optimization pro

窗帘等

Standard Bundle Methods: Untrusted Models and Dualitypproaches are based on constructing models of the function, but lack of continuity of first-order information implies that these models cannot be trusted, not even close to an optimum. Therefore, many different forms of stabilization have been proposed to try to avoid being led to areas where the mo

发现

A Second Order Bundle Algorithm for Nonsmooth, Nonconvex Optimization Problems method by Fendl and Schichl (A feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints: I. derivation and convergence. arXiv:1506.07937, 2015, preprint) to the general nonlinearly constrained case. Instead of using a penalty function or a fi