Algorithms and software for large scale nonlinear optimization
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Algorithms and Software for Large-Scale Nonlinear Optimization. OTC day, 6 Nov 2003 Richard Waltz, Northwestern University Project I : Large-scale Active-Set methods for NLP Fact or Fiction ? (with J. Nocedal, R. Byrd and N. Gould) Project II :

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Algorithms and software for large scale nonlinear optimization
Algorithms and Software for Large-Scale Nonlinear Optimization

OTC day, 6 Nov 2003

Richard Waltz, Northwestern University

  • Project I:

    Large-scale Active-Set methods for NLP Fact or Fiction?

    (with J. Nocedal, R. Byrd and N. Gould)

  • Project II:

    Adaptive Barrier Updates for NLP Interior-Point methods

    (with J. Nocedal, R. Byrd, and A. Waechter)


Current active set methods
Current Active-Set Methods

  • Successive Linear Programming (SLP)

    • Inefficient, slow convergence

  • Successively Linearly Constrained (SLC)

    • e.g. MINOS

    • Difficulty scaling up

  • Sequential Quadratic Programming (SQP)

    • e.g. filterSQP, SNOPT

    • Very robust when less than a couple thousand degrees of freedom

    • For larger problems QP subproblems may be too expensive


Slp eqp approach
SLP-EQP Approach

  • Fletcher, Sainz de la Maza (1989)

    Overview

    0. Given: x

  • Solve LP to get working setW.

  • Compute a step, d, by solving an equality constrainedQP using constraints in W.

  • Set: xT= x+d.


Slp eqp
SLP-EQP

  • Strengths:

    • Only solve LP and EQP subproblems

    • Early results very encouraging

    • Competitive with SQP – able to solve problems with more degrees of freedom

  • But…

    • Not yet competitive with Interior

    • Difficulties in warm starting LP subproblems

    • How to handle degeneracy?

    • Theory needs more development


Adaptive barrier updates
Adaptive barrier updates

NLP

  • Functions twice continuously differentiable


Adaptive barrier updates1
Adaptive barrier updates

Solve a sequence of barrier subproblems

  • Approach solution to NLP as


Adaptive barrier updates nlp
Adaptive barrier updates (NLP)

Overview of Barrier Strategies:

  • Fixed decrease with barrier stop test (e.g. KNITRO)

  • Centrality-based strategies (e.g. LOQO)

  • Probing strategies (e.g. Mehrotra PC)


Adaptive barrier updates nlp1
Adaptive barrier updates (NLP)

KNITRO

  • Conservative rule

    • Initially m=0.1

    • Decrease m linearly

    • Fastlinear decrease near solution

  • Globally convergent

  • Robust but trade-off some efficiency

  • Initial point option


Adaptive barrier updates nlp2
Adaptive barrier updates (NLP)

  • Develop a more flexible adaptive rule

    • Allow increases in barrier parameter!

  • q : function of:

    Spread of complementarity pairs

    Recent steplengths

    Ease of meeting a barrier stop test

    Probing step (e.g. predictor step)


Globally convergent framework
Globally Convergent Framework

  • Official mfor global conv (satisfies barrier stop test)

  • Trial m for flexibility

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