Efficient Global Optimization

⚠️ Curated Limitations & Negative Results

• This identity denotes the original deterministic scalar procedure, not every Bayesian optimizer or every method using EI. No noisy-objective, nonlinear-constraint, derivative-enabled, multifidelity, batch or multiobjective extension is absorbed. Section 6, PDF p.33 / printed p.487 discusses such extensions separately and leaves noisy-function EGO unresolved. EI itself is a distinct acquisition rule; TPE and SMAC use different model and search machinery.
• The source does not prove global convergence. Conjecture 1 assumes correlation parameters theta_h bounded away from zero, a continuous objective on a finite box and an indefinitely continued search; it remains explicitly unproved (Section 4.2, PDF p.22 / printed p.476). Acquisition bounds, empirical examples and a model-based stopping threshold do not establish finite-budget optimality or universal performance.
• Nonlinear response transformations can change improvement magnitudes and query rankings. The literal 1% stopping rule needs a sign and scale convention when the incumbent is zero or negative; no absolute-value replacement or numerical floor is silently supplied. The log-scale tolerance is described as an approximate relative change. Plug-in uncertainty and one-step gain also limit interpretation of that stopping rule (Section 4.2, PDF pp.19–21 / printed pp.473–475).
• Very smooth responses and closely spaced inputs can make R nearly singular. The authors report singular-value decomposition with small singular values set to zero, but the record does not certify a particular truncation threshold, ordinary-inverse validity after truncation, or preservation of all interpolation and bounding properties (Section 6, PDF p.32 / printed p.486).
• Appendix 1, PDF p.36 / printed p.490, changes the negative cross term of the displayed quadratic into a positive term in its derivative. Differentiation requires a minus sign to recover the stated predictor Eq.7. The inspected discrepancy and separate exact sign witness are retained as source algebra context, not an asserted author erratum or a repaired EGO implementation.
• For fixed real symmetric positive-definite R, fixed nonnegative process variance and exact arithmetic, the Eq.16 Hessian is positive semidefinite with a zero eigenvalue, so the Eq.17 alpha correction is zero. The separate curator derivation uses A = R_inverse - (R_inverse 1)(R_inverse 1)^T/(1^T R_inverse 1). This qualifies the source discussion of a possible negative eigenvalue. Nonlinear constraints linking r and x remain nonconvex; neither EI concavity, convexity of the full search problem nor a numerical failure in the authors’ implementation follows (Section 4.3, PDF pp.22–24 / printed pp.476–478; Appendix 2, PDF p.36 / printed p.490).
• Primary method evidence is the 38-page journal-layout mirror of the 1998 paper. The distinct 43-page author manuscript was cover-inspected only; exact equivalence to that manuscript or an inaccessible publisher download was not established. The cited Mockus et al. (1978) chapter was not read, so no earliest-invention claim is made.
• The supporting original calculations and separate root reproductions check bounded EI, interpolation and source-sign examples. Exact rational checks are distinct from floating Gaussian, quadrature and transformation calculations. The separate Hessian assessment is an analytic derivation under stated assumptions. None executes author code, implements the complete EGO search, replicates its benchmarks or supplies a formal erratum or convergence proof.