Feasible directions algorithms for optimization problems with equality and inequality constraints

1976 ◽  
Vol 11 (1) ◽  
pp. 67-80 ◽  
Author(s):  
D. Q. Mayne ◽  
E. Polak
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Feasible Directions ◽  
Equality And Inequality Constraints

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

scholarly journals A Full Rank Condition for Continuous-Time Optimization Problems with Equality and Inequality Constraints

2019 ◽  
Vol 20 (1) ◽  
pp. 15 ◽  
Author(s):  
Moisés Rodrigues Cirilo Monte ◽  
Valeriano Antunes De Oliveira
Keyword(s):  
Continuous Time ◽  
Regularity Condition ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Full Rank ◽  
Rank Condition ◽  
Time Optimization ◽  
Equality And Inequality Constraints

First and second order necessary optimality conditions of Karush-Kuhn-Tucker type are established for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit function theorem are used in order to achieve such necessary conditions.

Feasible and Optimal Designs of Variable Air Gap Torque Motors

1991 ◽  
Vol 113 (2) ◽  
pp. 241-245 ◽  
Author(s):  
M. C. Leu ◽  
R. A. Aubrecht
Keyword(s):  
Power Consumption ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Physical Characteristics ◽  
Air Gap ◽  
Numerical Results ◽  
Optimal Designs ◽  
Constrained Optimization Problems ◽  
Equality And Inequality Constraints

The problems of automating the feasible and optimal designs of variable air gap torque motors are studied. Both are formulated as constrained optimization problems, where equality and inequality constraints are associated with the geometrical and physical characteristics of the device. Numerical results show that feasible designs can be obtained for specified rated torque outputs, and optimal designs can be achieved by reducing the volume or power consumption substantially from the initial designs, without reducing the rated torque output.

scholarly journals Strong complementary approximate Karush-Kuhn-Tucker conditions for multiobjective optimization problems

2021 ◽  
pp. 24-24
Author(s):  
Jitendra Maurya ◽  
Shashi Mishra
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
Multiobjective Optimization Problems ◽  
Sequential Optimality Conditions ◽  
Equality And Inequality Constraints ◽  
Optim Theory

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications and introduce a weak constraint qualification which assures the equivalence between SCAKKT and the strong Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483{500, 1994) conditions for multiobjective optimization problems.

scholarly journals Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yuefang Lian ◽  
Jinchuan Zhou ◽  
Jingyong Tang ◽  
Zhongfeng Sun
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Necessary Condition ◽  
Sensing Matrix ◽  
Quadratic Constraint ◽  
Linear Equality ◽  
Equality And Inequality Constraints ◽  
Measurement Vector ◽  
The Stability ◽  
Sufficient And Necessary Condition

1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.

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