An Algorithmic Approach to Nonlinear Analysis and Optimization (Edward J. Beltrami); The Approximate Minimization of Functionals (James W. Daniel); Approximate Methods in Optimization Problems (Vladimir F. Demyanov and Aleksandr M. Rumnov); Computational Methods in Optimization : A Unified Approach (E. Polak); Necessary Conditions for an Extremum (N. Pshenichnyi)

SIAM Review ◽  
1977 ◽  
Vol 19 (2) ◽  
pp. 341-358
Author(s):  
M. Z. Nashed
Keyword(s):  
Nonlinear Analysis ◽  
Computational Methods ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Unified Approach ◽  
Approximate Methods ◽  
Algorithmic Approach ◽  
Approximate Minimization

A Unified Approach to Robust Farkas-Type Results with Applications to Robust Optimization Problems

2017 ◽  
Vol 27 (2) ◽  
pp. 1075-1101 ◽  
Author(s):  
N. Dinh ◽  
T. H. Mo ◽  
G. Vallet ◽  
M. Volle
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Unified Approach

scholarly journals Optimal Stopping for Processes with Independent Increments, and Applications

2009 ◽  
Vol 46 (04) ◽  
pp. 1130-1145 ◽  
Author(s):  
G. Deligiannidis ◽  
H. Le ◽  
S. Utev
Keyword(s):  
Optimal Stopping ◽  
Optimization Problems ◽  
Infinite Horizon ◽  
Unified Approach ◽  
Reward Function ◽  
Finance Industry ◽  
Independent Increments ◽  
Reward Functions ◽  
First Time ◽  
The Value Function

In this paper we present an explicit solution to the infinite-horizon optimal stopping problem for processes with stationary independent increments, where reward functions admit a certain representation in terms of the process at a random time. It is shown that it is optimal to stop at the first time the process crosses a level defined as the root of an equation obtained from the representation of the reward function. We obtain an explicit formula for the value function in terms of the infimum and supremum of the process, by making use of the Wiener–Hopf factorization. The main results are applied to several problems considered in the literature, to give a unified approach, and to new optimization problems from the finance industry.

scholarly journals On solution sets of nonconvex Darboux problems and applications to optimal control with endpoint constraints

1996 ◽  
Vol 37 (3) ◽  
pp. 354-391 ◽  
Author(s):  
H. D. Tuan
Keyword(s):  
Constraint Qualification ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Regularity Assumption ◽  
Darboux Problem ◽  
Continuous Version ◽  
Open Mapping Theorem ◽  
Solution Sets ◽  
Relaxation Theorem ◽  
Endpoint Constraints

AbstractWe prove a continuous version of a relaxation theorem for the nonconvex Darboux problem xlt ε F(t, τ, x, xt, xτ). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.

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