scholarly journals Hadamard directional differentiability of the optimal value of a linear second-order conic programming problem

2017 ◽  
Vol 13 (5) ◽  
pp. 0-0
Author(s):  
Qingsong Duan ◽  
◽  
Mengwei Xu ◽  
Liwei Zhang ◽  
Sainan Zhang ◽  
...  
Keyword(s):  
Programming Problem ◽  
Second Order ◽  
Conic Programming ◽  
Directional Differentiability ◽  
Optimal Value ◽  
Hadamard Directional Differentiability

Hadamard Directional Differentiability of the Optimal Value Function of a Quadratic Programming Problem

2018 ◽  
Vol 35 (03) ◽  
pp. 1850012 ◽  
Author(s):  
Sainan Zhang ◽  
Liwei Zhang ◽  
Hongwei Zhang ◽  
Qingsong Duan
Keyword(s):  
Quadratic Programming ◽  
Value Function ◽  
Convex Sets ◽  
Compact Convex ◽  
Optimal Solution ◽  
Optimal Value Function ◽  
Directional Differentiability ◽  
Optimal Value ◽  
Hadamard Directional Differentiability ◽  
Wolfe Dual

In this paper, we consider the stability analysis of a convex quadratic programming (QP) problem and its restricted Wolfe dual when all parameters in the problem are perturbed. Based on the continuity of the feasible set mapping, we establish the upper semi-continuity of the optimal solution mappings of the convex QP problem and the restricted Wolfe dual problem. Furthermore, by characterizing the optimal value function as a min–max optimization problem over two compact convex sets, we demonstrate the Lipschitz continuity and the Hadamard directional differentiability of the optimal value function.

scholarly journals Second-Order Variational Analysis in Conic Programming with Applications to Optimality and Stability

2015 ◽  
Vol 25 (1) ◽  
pp. 76-101 ◽  
Author(s):  
Boris S. Mordukhovich ◽  
Jiří V. Outrata ◽  
Héctor Ramírez C.
Keyword(s):  
Variational Analysis ◽  
Second Order ◽  
Conic Programming

scholarly journals A Global Optimization Algorithm for Sum of Linear Ratios Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yuelin Gao ◽  
Siqiao Jin
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Programming Problem ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Bilinear Programming ◽  
Global Optimization Algorithm ◽  
Product Function ◽  
Optimal Value

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

scholarly journals On weak Hadamard differentiability of convex functions on Banach spaces

1996 ◽  
Vol 54 (1) ◽  
pp. 155-166 ◽  
Author(s):  
J.R. Giles ◽  
Scott Sciffer
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Functions ◽  
Directional Differentiability ◽  
Hadamard Differentiability ◽  
Hadamard Directional Differentiability

We study two variants of weak Hadamard differentiability of continuous convex functions on a Banach space, uniform weak Hadamard differentiability and weak Hadamard directional differentiability, and determine their special properties on Banach spaces which do not contain a subspace topologically isomorphic to l1.

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