Corrigendum: “on the directional derivative of the optimal solution mapping without linear independence constraint qualification” of S. Dempe (optimization 20 (1989) 4 401–414)

Optimization ◽  
1991 ◽  
Vol 22 (3) ◽  
pp. 417-417
Author(s):  
S. Dempe
Keyword(s):  
Constraint Qualification ◽  
Linear Independence ◽  
Directional Derivative ◽  
Optimal Solution ◽  
Solution Mapping ◽  
Linear Independence Constraint Qualification

scholarly journals Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 12 ◽  
Author(s):  
Xiangkai Sun ◽  
Hongyong Fu ◽  
Jing Zeng
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Sufficient Optimality Conditions ◽  
Convex Constraint ◽  
Approximate Optimality Conditions ◽  
Necessary And Sufficient

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

3-1 Piecewise NCP Function for New Nonmonotone QP-Free Infeasible Method

2014 ◽  
Vol 26 (5) ◽  
pp. 566-572 ◽  
Author(s):  
Ailan Liu ◽  
◽  
Dingguo Pu ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Ncp Function ◽  
Line Searches ◽  
Complementarity Condition ◽  
Linear Independence Constraint Qualification ◽  
Systems Of Linear Equations

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260005/04.jpg"" width=""300"" />Algorithm flow chart</div> We propose a nonmonotone QP-free infeasible method for inequality-constrained nonlinear optimization problems based on a 3-1 piecewise linear NCP function. This nonmonotone QP-free infeasible method is iterative and is based on nonsmooth reformulation of KKT first-order optimality conditions. It does not use a penalty function or a filter in nonmonotone line searches. This algorithm solves only two systems of linear equations with the same nonsingular coefficient matrix, and is implementable and globally convergent without a linear independence constraint qualification or a strict complementarity condition. Preliminary numerical results are presented. </span>

scholarly journals Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Shaohua Pan ◽  
Shujun Bi ◽  
Jein-Shan Chen
Keyword(s):  
Constraint Qualification ◽  
Optimal Solution ◽  
Second Order ◽  
Strong Regularity ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Constraint Nondegeneracy ◽  
Robinson’S Constraint Qualification ◽  
Locally Optimal Solution

This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.

scholarly journals Smoothing approximations to nonsmooth optimization problems

1995 ◽  
Vol 36 (3) ◽  
pp. 274-285 ◽  
Author(s):  
X.Q. Yang
Keyword(s):  
Optimization Problems ◽  
Directional Derivative ◽  
Optimal Solution ◽  
Necessary Optimality Conditions ◽  
Second Order ◽  
Smooth Approximation ◽  
Minimization Problems ◽  
Second Order Directional Derivative ◽  
Nonsmooth Minimization ◽  
Original Objective

AbstractWe study certain types of composite nonsmooth minimization problems by introducing a general smooth approximation method. Under various conditions we derive bounds on error estimates of the functional values of original objective function at an approximate optimal solution and at the optimal solution. Finally, we obtain second-order necessary optimality conditions for the smooth approximation prob lems using a recently introduced generalized second-order directional derivative.

scholarly journals MPCC: Strong Stability of M-stationary Points

2021 ◽  
Author(s):  
Harald Günzel ◽  
Daniel Hernández Escobar ◽  
Jan-J. Rückmann
Keyword(s):  
Stationary Point ◽  
Constraint Qualification ◽  
Local Existence ◽  
Strong Stability ◽  
Stationary Points ◽  
Algebraic Characterization ◽  
Describing Functions ◽  
Mathematical Programs ◽  
Local Existence And Uniqueness ◽  
Linear Independence Constraint Qualification

AbstractIn this paper we study the class of mathematical programs with complementarity constraints MPCC. Under the Linear Independence constraint qualification MPCC-LICQ we state a topological as well as an equivalent algebraic characterization for the strong stability (in the sense of Kojima) of an M-stationary point for MPCC. By allowing perturbations of the describing functions up to second order, the concept of strong stability refers here to the local existence and uniqueness of an M-stationary point for any sufficiently small perturbed problem where this unique solution depends continuously on the perturbation. Finally, some relations to S- and C-stationarity are briefly discussed.

scholarly journals Duality without constraint qualification in nonsmooth optimization

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
S. Nobakhtian
Keyword(s):  
Constraint Qualification ◽  
Dual Problem ◽  
Directional Derivative ◽  
Inequality Constraints ◽  
Generalized Convex Functions ◽  
Primal Problem ◽  
Necessary Conditions For Optimality ◽  
Nonsmooth Multiobjective Optimization ◽  
Sufficient And Necessary Conditions ◽  
Convexity Assumptions

We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality results are obtained without a constraint qualification.

Identifying Measurement Invariant Item Sets in Cross-Cultural Settings Using an Automated Item Selection Procedure

Methodology ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 177-188 ◽  
Author(s):  
Martin Schultze ◽  
Michael Eid
Keyword(s):  
Measurement Invariance ◽  
Optimal Solution ◽  
Selection Procedure ◽  
Cross Cultural ◽  
Item Selection ◽  
Ant System ◽  
Item Quality ◽  
Ant System Algorithm ◽  
Selection For ◽  
Selection Of

Abstract. In the construction of scales intended for the use in cross-cultural studies, the selection of items needs to be guided not only by traditional criteria of item quality, but has to take information about the measurement invariance of the scale into account. We present an approach to automated item selection which depicts the process as a combinatorial optimization problem and aims at finding a scale which fulfils predefined target criteria – such as measurement invariance across cultures. The search for an optimal solution is performed using an adaptation of the [Formula: see text] Ant System algorithm. The approach is illustrated using an application to item selection for a personality scale assuming measurement invariance across multiple countries.

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