Convergence of the CA algorithm for nonlinear programs

1999 ◽  
pp. 135-168
Author(s):  
Michael Patriksson
Keyword(s):  
Nonlinear Programs

PLANNING FOR ACCELERATED LIFE TESTS

1999 ◽  
Vol 06 (03) ◽  
pp. 265-275 ◽  
Author(s):  
LOON-CHING TANG
Keyword(s):  
Acceleration Factor ◽  
Test Time ◽  
Initial Sample ◽  
Lower Stress ◽  
Nonlinear Programs ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Stress Levels ◽  
Life Tests ◽  
Sample Allocation

We present two alternative perspectives to the current way of planning for constant-stress accelerated life tests (CSALTs) and step-stress ALT (SSALT). In 3-stress CSALT, we consider test plans that not only optimize the stress levels but also optimize the sample allocation. The resulting allocations also limit the chances of inconsistency when data are plotted on a probability plot. For SSALT, we consider test plans that not only optimize both stress levels and holding times, but also achieve a target acceleration factor that meets the test time constraint with the desirable fraction of failure. The results for both problems suggest that the statistically optimal way to increase acceleration factor in an ALT is to increase lower stress levels and; in the case of CSALT, to decrease their initial sample allocations; in the case of SSALT, to reduce their initial hold times. Both problems are formulated as constrained nonlinear programs.

scholarly journals Mixed Integer NonLinear Programs featuring “On/Off” constraints: convex analysis and applications

2010 ◽  
Vol 36 ◽  
pp. 1153-1160 ◽  
Author(s):  
Hassan Hijazi ◽  
Pierre Bonami ◽  
Gérard Cornuéjols ◽  
Adam Ouorou
Keyword(s):  
Convex Analysis ◽  
Mixed Integer ◽  
Nonlinear Programs

scholarly journals Symmetric dual nonlinear programs

1965 ◽  
Vol 15 (3) ◽  
pp. 809-812 ◽  
Author(s):  
George Dantzig ◽  
E. Eisenberg ◽  
Richard Cottle
Keyword(s):  
Nonlinear Programs

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 note on embeddings for the Augmented Lagrange Method

2010 ◽  
Vol 20 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Gemayqzel Bouza-Allende ◽  
Jurgen Guddat
Keyword(s):  
Augmented Lagrangian ◽  
Equality Constraints ◽  
Embedding Problem ◽  
Lagrange Method ◽  
Parametric Problem ◽  
Nonlinear Programs ◽  
Augmented Lagrange Method ◽  
Quadratic Perturbation ◽  
Lagrangian Embedding

Nonlinear programs (P) can be solved by embedding problem P into one parametric problem P(t), where P(1) and P are equivalent and P(0), has an evident solution. Some embeddings fulfill that the solutions of the corresponding problem P(t) can be interpreted as the points computed by the Augmented Lagrange Method on P. In this paper we study the Augmented Lagrangian embedding proposed in [6]. Roughly speaking, we investigated the properties of the solutions of P(t) for generic nonlinear programs P with equality constraints and the characterization of P(t) for almost every quadratic perturbation on the objective function of P and linear on the functions defining the equality constraints.

Sign in / Sign up

Export Citation Format

Share Document