Fields Institute Informal Working Group on Validated Methods for Optimization
Schedule

Prepared by George Corliss, May 27-31, 2002

Workshop entry page: www.fields.toronto.edu/programs/scientific/01-02/numerical/optimization

Raw schedule photo
Index to photos of our blackboard notes
Photos of George's handwritten notes

Topics: (photo)

Enclosures			Applications
	Taylor models			Financial
	Bernstein, Garloff, Griewank			Geometric, combinatorial
	Big boxes: efficient f([X]) - c <= 0			Tucker, reachability sets
	Enclosure trade-offs			Optimal control
				Killers? Blockbusters?
Techniques for optimization			Supporting techniques
	Share, trade-off, synergies			Policy on "interval"
	Accelerations			Baker's SIAM Review article
	Randomizations			Computing with probabilities
	Multi-precision, blow, Ax=b
	Linear LP, Singular Fritz-John			Photos of raw suggestions: 1, 2, 3

Daily schedule:
      9:30 Begin
      10:30 Coffee
      12:00 Lunch
      1:30 Resume
      3:00 Tea

Monday, May 27, AM

• Ken: Introduction to the Fields Institute [George's notes]
• George: Set agenda - "If you would help me, what would I ask you to do?"
  Photos of raw suggestions: 1, 2, 3
  Topics photo
  Raw schedule photo
• Bill: Policy on "interval" [George's notes]
  Take-away: Can we adopt a policy defining "interval" to mean validated with directed rounding?

Monday, May 27, PM

• Baker: SIAM Review article [George's notes]
  Take-away: Focus on 2-3 impressive applications
• Vladik: Computing with probabilities. Photos: 1, 2, 3, 4, 5, 6, 7, 8. [George's notes p2, p3, p4, p5]
• Bill: Computing with probabilities [George's notes p5]
• George: Issue on Taylor models
  Arnold's paper is at http://www.mat.univie.ac.at/~neum/papers.html#taylor
  George's clustering of issues

Tuesday, May 28, AM. Photo of schedule

• Tibor: Bernstein polynomials for enclosures. Photos: 1, 2, 3, 4, 5, 6, 7 [George's notes p6, p7]
• Ned & Vladik: Optimal basis functions [George's notes p7]
• Mihály: Application - Packing circles in a square. Photos: 1, 2 [George's notes p7]

Tuesday, May 28, PM

• Bill: Focus
• Martin & Kyoko: Taylor models - Roundoff. Photos: 1, 2, 3, 4 [George's notes p8, p9, p10, p11, p12, p13, p14, p15, p16]

Wednesday, May 29, AM. Photo of schedule

• Applications:
  • Mihály (cont.): Application - Packing circles in a square. Photos: 1, 2, 3 [George's notes p16A]
  • Ned: Taylor models on x_{n+1} = A x_n [George's notes p16A]
  • Ned: Reachability. Photos: 1, 2, 3, 4, 5, 6, 7, 8
  • George: "All together" for optimal control. Photo: 1 [George's notes p16A]

Wednesday, May 29, PM

• Martin & Kyoko: Taylor models - Wrapping and shrink wrapping. Photos: 1, 2 [George's notes p17, p18, p19]
• Martin & Kyoko: Taylor models - Order of convergence. Photos: 1, 2 [George's notes p19, p20, p21, p22]

Thursday, May 30, AM. Photo of schedule

• Optimization techniques
  • Tibor: Integration of tools. Photos: 1, 2 [George's notes p22A, p23, p24]
  • Tibor: Empirical convergence order
  • George: Randomizations. Photos: 1

Thursday, May 30, PM

• Optimization techniques
  • Natalie: Multi-precision, blow, Ax = b. Photos: 1, 2, 3, 4 [George's notes p24, p25]
  • Baker: Nonlinear mini-max - Singular Fritz-John. Photos: 1, 2 [George's notes p25, p26]
  • Baker: Jansson's validated LP [George's notes p26]
  • Bill: Big boxes: f([X]) - c <= 0; Term concistency [George's notes p26, p27]
  • Bill: Solving over-determined systems. Photos: 1, 2, 3 [George's notes p27, p28]
    To accomplish IF (f([x]) > fBar) delete [x]
    Compute min f(x), x in [x]
    subject to f(x) <= fBar
    If EMPTY return TRUE; if any feasible return FALSE

Friday, May 31, AM. Photo of schedule

• Kyoko: By hand TM for a linear system. Photos: 1, 2, 3, 4, 4, 3A, 5A, 6, 2A, 8, 9 [George's notes p28.1, p29, p30]

Friday, May 31, PM

• George: Neural networks. Photo: 1
• Baker: Peeling and GlobSol. Photos: 1, 2, 3, 4, 5
• Petter: Financial. Photos: 1, 2, 3, 4
• Jeff: GrafEQ. Photos: 1, 2, 3, 4 5, 6, 7

Saturday, June 1, AM

• Natalie: Demo. See www.ens-lyon.fr/~jmmuller/Intro-TMD.html (Not found?). Photos: 1, 2
• Baker: GlobSol. See interval.louisiana.edu/preprints.html, click on [Talks]. Photos: 1, 2
• Bill: Csets. Photos: 1, 2, 3, 4, 5, 6, 7, 8

• Discussion looses focus ==> "Rat hole" ==> move on
• Aggressive facilitator ==> "Shut up and sit down!"

Some mentioned applications of global optimization:

• Compute bounds of Cummulative Density Functions
• ASCI nuclear weapons/power plant simulations
• Building engineering
• Drug trials
• Bounded errors modeling in medical instrument
• Confidential work at several major European companies
• Siting of landfills
• DSP - Characterizing speech

We thank the Fields Institute for its generous support and encouragement