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Optimization Interview Questions

Optimization is where math meets money on a trading desk: almost every quant decision is secretly an argmax or argmin. This playlist builds you from the bedrock ideas (convexity, first-order conditions, the Hessian/second-order test, Lagrange multipliers and KKT) up through the workhorses you will a

92 Problems 2 Easy 53 Medium 37 Hard
A curated set of 92 optimization problems drawn from our bank — the kind that actually shows up in quant interviews, rewritten for clarity with worked solutions we author ourselves. We never claim a wording is verbatim. 13 are free to open and fully solve.

How to think about optimization questions

Optimization problems share one skeleton: you want the best value subject to constraints, and the trick is never brute force — it's recognizing the shape of the landscape so the optimum reveals where it must sit.

CONVEXITY IS THE GIFT

If the objective is convex and the feasible set is convex, any local minimum is the global one — so you just chase the gradient downhill until it vanishes. Half the battle in these problems is spotting that hidden convexity (or a substitution that creates it).

PRICE THE CONSTRAINTS

To handle constraints, attach a Lagrange multiplier to each — the marginal value of relaxing it. At the optimum the objective's gradient is a combination of the constraint gradients, and the KKT conditions package equality, inequality, and complementary-slackness cases into one tidy system.

Work this set and the question becomes reflexive: is this convex, and what is each constraint worth at the margin?

Optimization questions (92)

Optimization interview questions FAQ

What kind of optimization questions show up in quant interviews?

This page collects 92 optimization problems that recur in quant trading and research interviews, each with a full worked solution and the intuition behind it. They range from quick warmups to the harder variants firms use to separate candidates.

How hard are optimization interview questions?

The set spans 2 easy, 53 medium and 37 hard problems. Most sit at medium difficulty — a few minutes of clean reasoning — with a harder tail that rewards knowing the canonical approach rather than grinding.

How should I practice optimization for quant interviews?

Work through them by difficulty, starting just below your level, and write the solution out before checking. 13 are free to open with the full worked solution, so you can judge the quality first. Focus on the recurring patterns rather than memorizing answers — the same handful of ideas generate most variants.

Are these real quant interview questions?

They are a curated set drawn from our problem bank — the kind of optimization question that actually appears in quant interviews, rewritten for clarity with solutions we author ourselves. We don't claim any single wording is verbatim, and every problem carries a full solution.

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