Local minimum
Description
A point in an optimization landscape where every nearby direction looks worse — yet the global landscape has better attractors elsewhere. The local-gradient reading says “stay where you are; every step is uphill”; the global reading says “you’re stuck in a small basin; better territory exists, but you can’t see it from here.” The cognitive correlate: “every direction I can look in is worse, but I suspect I’m stuck.” The concept picks out a specific structural shape: locally-optimal AND globally-suboptimal AND the-local-view-doesn’t-disclose-the-fact. It’s distinct from “you’re at the global optimum” (no escape needed) and from “you’re in a bad place and can see better territory” (just go). Local-minimum is the trap, not the position.Triggers
User-initiated: User says “we’re stuck,” “every option is worse,” “I don’t see how to improve from here,” but with a sense that things should be better. Vocabulary cues: “stuck,” “rut,” “every direction is worse,” “local optimum.” Agent-initiated: Agent notices that incremental search from here is failing and that the right move might require accepting a locally-worse step. Candidate inference: “you might be in a local minimum; what is a deliberate disruption that takes you out?” Situation-shape signals: Long-running optimization plateaus. Strategy discussions where every named alternative is rejected as worse. “We’ve tried everything” rhetoric.Exclusions
- Convex landscapes — in convex optimization, local-minimum = global-minimum. The concept doesn’t fire; the trap doesn’t exist.
- No defined objective function — if you can’t even articulate what “better” means, local-minimum is the wrong question; the upstream problem is goal articulation.
- Genuine global optimum — sometimes you’re not stuck; you’re just at the best you can do. Don’t impose “local minimum” framing on a goal that is actually fulfilled.
Structure
Relationships
- gradient — local-minimum is the failure mode of pure gradient-following.
- attractor — local-minimum is a small attractor basin; recognizing it requires distinguishing local from global.
- spike — spikes are the deliberate-locally-bad move that escapes; literally the technique.
- loop-completion — sometimes you’re in a local minimum because your loop hasn’t closed enough to read the wider landscape.
- doctrine — doctrines often prescribe periodic disruption (offsites, code rewrites, rotation) explicitly to defeat local-minimum traps.
Examples
Gradient-descent stuck in optimization · computer-science
Gradient-descent stuck in optimization · computer-science
neural network training, classical optimization; landscapes with many small basins.
Career stuck at a job that pays okay · psychology
Career stuck at a job that pays okay · psychology
local-gradient reading: every alternative I can see pays less or is more risk. Global reading: maybe wrong.
Greedy algorithms · computer-science
Greedy algorithms · computer-science
greedy is the strategy that always gets caught in local minima; the canonical algorithmic case.
Optimization theory / numerical analysis; gradient-descent literature; reinforcement-learning exploration-exploitation tradeoffs · computer-science
Optimization theory / numerical analysis; gradient-descent literature; reinforcement-learning exploration-exploitation tradeoffs · computer-science
foundational primitive in optimization across every domain that has objective functions
Product local-minimum · business
Product local-minimum · business
incremental optimization over years; UI gets better by each metric while the overall shape is still wrong.
Reinforcement learning: exploration-exploitation tradeoff is the local-vs-global tension at the policy-learning level. · computer-science
Reinforcement learning: exploration-exploitation tradeoff is the local-vs-global tension at the policy-learning level. · computer-science
Reinforcement learning: exploration-exploitation tradeoff is the local-vs-global tension at the policy-learning level.
Simulated annealing (Kirkpatrick et al. 1983) — the canonical algorithmic technique for escaping local minima via delibe · computer-science
Simulated annealing (Kirkpatrick et al. 1983) — the canonical algorithmic technique for escaping local minima via delibe · computer-science
Kirkpatrick, Gelatt, and Vecchi’s 1983 Science paper introduced simulated annealing as a stochastic optimization technique modeled on the physical process of slowly cooling a material to find its low-energy crystalline state. The algorithm accepts worse moves with probability that decreases as the simulated “temperature” cools — at high temperature the search explores broadly (jumping out of basins of attraction), at low temperature it converges to a local minimum. The schedule of temperature decrease is the design lever that controls the explore-exploit tradeoff.Inference: Simulated annealing is the canonical escape mechanism for local minima, and the metaphor itself encodes the structural shape: temperature is the noise floor; the optimization surface has multiple basins; the goal is to find a deeper basin than the one you started in. The same structural shape transfers to research strategy (deliberately consider implausible directions for a while to avoid getting stuck refining mediocre ones), team hiring (deliberate weirdness in candidate selection to avoid type-monoculture), and product roadmapping (periodic “what if we did the opposite” sessions to escape local product strategies). When invoking
local-minimum, also invoke the question “what is the temperature schedule that would let us escape?” — the answer specifies the corrective move.Software-architecture local-best decisions · computer-science
Software-architecture local-best decisions · computer-science
every refactor we can think of from here is worse; but the right move was three architectural decisions ago.