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IBM

MCP Math Server

by IBM

nelder_mead

Optimize mathematical functions without derivatives using the Nelder-Mead simplex algorithm. Input your function and initial guess to find minima or maxima.

Instructions

Perform Nelder-Mead simplex algorithm for derivative-free optimization (Domain: numerical, Category: optimization)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
fYes
x0Yes
alphaNo
gammaNo
rhoNo
sigmaNo
max_iterationsNo
toleranceNo
Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries full burden. It mentions the algorithm type and optimization context but lacks critical behavioral details: it doesn't specify what the tool returns (e.g., optimal point, iterations), error handling, convergence behavior, or computational characteristics. For a complex optimization tool with 8 parameters, this is a significant gap.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded in a single sentence, with no wasted words. Every part ('Perform Nelder-Mead simplex algorithm for derivative-free optimization') contributes directly to the tool's purpose, and the domain/category annotations are efficiently appended.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of an optimization algorithm with 8 parameters, no annotations, and no output schema, the description is incomplete. It lacks essential context: what the tool returns, how to interpret results, parameter meanings, and usage examples. This makes it inadequate for effective agent invocation without external knowledge.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters1/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, and the description provides no information about any parameters. It doesn't explain what 'f' (the objective function), 'x0' (initial guess), or the Greek-letter parameters (alpha, gamma, rho, sigma) represent, nor does it cover 'max_iterations' and 'tolerance'. With 8 parameters and no schema descriptions, the description fails to add any semantic value.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Perform Nelder-Mead simplex algorithm for derivative-free optimization' with domain and category context. It specifies the verb ('Perform'), resource ('Nelder-Mead simplex algorithm'), and optimization context, but does not explicitly differentiate from sibling optimization tools like 'gradient_descent' or 'golden_section_search'.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No explicit guidance on when to use this tool versus alternatives is provided. The description mentions 'derivative-free optimization' which implies usage when derivatives are unavailable, but it doesn't name specific sibling tools or scenarios for comparison, leaving the agent without clear selection criteria.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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