Optimization / Mathematical Optimization
Mathematical Optimization
Optimization problems show up everywhere real decisions get made under limits: minimizing cost, maximizing output, scheduling scarce resources, routing efficiently. Getting from a real-world problem to a correctly formulated model — and then to a solver that actually converges on the right answer — is where most people get stuck. We help with both the formulation and the solving, and explain the result so it's usable, not just a black-box output.
This Is For You If...
You're a founder or analyst trying to optimize a real operational problem — scheduling, routing, resource allocation — and don't know where to start modeling it
You've built a model but your solver won't converge, returns an infeasible result, or takes far too long to run
You need help choosing the right optimization approach for a problem that doesn't obviously fit one category
You have a working solution but need help interpreting or explaining the result
Which Type of Optimization Fits Your Problem?
Ask Yourself | Points Toward |
Are your objective and constraints all linear, and can variables take any real value? | Linear Programming |
Do some or all variables need to be whole numbers (you can't have half a worker or 2.5 trucks)? | Integer Programming |
Is it a mix — some variables must be whole numbers, others can be continuous? | Mixed-Integer Programming |
Does your objective or any constraint involve a nonlinear relationship (products of variables, powers, ratios)? | Nonlinear Optimization |
Is your problem nonlinear but has a "bowl-shaped" structure that guarantees a single best solution? | Convex Optimization |
Is your problem defined more by finding any solution that satisfies a complex set of rules, rather than optimizing a single objective? | Constraint Optimization |
Not sure which fits? That's common — many real problems are a mix, or don't map cleanly onto textbook categories. Tell us the problem itself and we'll help identify the right formulation.
Optimization Services We Offer
Linear Programming
Linear programming (LP) problems — where the objective function and all constraints are linear — are the foundation of optimization, used for resource allocation, cost minimization, and production planning. We help formulate the objective and constraints correctly, choose the right solving method (simplex, interior point), and interpret the optimal solution, including sensitivity analysis when needed.
Integer Programming
Integer programming (IP) problems require some or all decision variables to take whole-number values — essential when fractional answers don't make real-world sense, like the number of staff to schedule or vehicles to deploy. We help formulate the integer constraints correctly and work through solving approaches like branch-and-bound, since integer problems are meaningfully harder to solve than their linear relaxations.
Mixed-Integer Programming
Mixed-integer programming (MIP) problems combine both integer and continuous variables in the same model — common in real scheduling, logistics, and facility-location problems where some decisions are binary or whole-number and others are continuous. We help build the combined formulation correctly and navigate solver performance, which can be a real challenge as MIP problems scale.
Nonlinear Optimization
Nonlinear optimization problems involve a nonlinear objective function or constraints — products of variables, exponents, ratios — which rules out standard linear solving methods. We help formulate the nonlinear model correctly and choose an appropriate solving approach, being clear about where global optimality can and can't be guaranteed.
Convex Optimization
Convex optimization covers the important special case of nonlinear problems where the objective and feasible region have the mathematical structure that guarantees any local optimum is also the global optimum. We help identify whether your problem is genuinely convex, formulate it to take advantage of that structure, and apply solving methods suited to it.
Constraint Optimization
Constraint optimization (or constraint satisfaction) problems focus on finding solutions that satisfy a complex set of rules and relationships, sometimes with an objective to optimize on top of that, sometimes just to find any feasible solution — common in scheduling, planning, and assignment problems. We help formulate the constraints correctly and choose an appropriate solving technique for the problem's actual structure.
Not sure your problem fits neatly into one of these? Most real optimization problems blend elements of several — tell us what you're working with and we'll help identify the right approach.
What We Need From You
What to Share | Why It Helps |
A description of the actual problem you're trying to solve | The real-world problem, not just the math, is what determines the right formulation |
Any existing formulation, model, or code you've already built | Lets us build on what you have rather than starting from scratch |
The specific objective (what you're minimizing or maximizing) | Central to formulating the model correctly |
The constraints/limitations involved | Missing or incorrect constraints are one of the most common sources of a wrong or infeasible model |
Whether this is for research or a real operational problem | Changes the expected level of rigor, explanation, and practical constraints involved |
Any deadline you're working with | Helps us scope the right turnaround |
Common Mistakes to Avoid
Instinct | Why It Doesn't Help | Do This Instead |
Treating a genuinely nonlinear relationship as linear to simplify the model | Produces a model that doesn't actually represent the real problem, leading to a wrong or misleading solution | Formulate the model to match the real relationships, even if that means a harder solving approach |
Assuming a nonlinear problem's local optimum is the global optimum | Only guaranteed for convex problems — for general nonlinear problems, a solver can get stuck at a solution that isn't actually best | Confirm whether your problem is convex, and if not, use methods appropriate for finding or approximating the global optimum |
Relaxing integer constraints to "just solve it as linear" without understanding the implications | Can produce fractional results that don't make sense for the real problem, and doesn't tell you how to round correctly | Solve the integer problem properly, or understand exactly how to interpret a relaxed solution if that's a deliberate step |
Adding constraints without checking whether the problem remains feasible | Can result in a model with no valid solution at all, without an obvious explanation why | Check feasibility incrementally as constraints are added, especially in complex constraint optimization problems |
Assuming solver non-convergence means the model is wrong | Can also mean the problem is poorly scaled, the solver's settings need tuning, or the problem is simply hard for its size | Diagnose whether the issue is the formulation, the scaling, or the solving approach before rewriting the model |
Skipping sensitivity analysis on an LP/MIP result | Means you don't know how robust the "optimal" answer actually is to small changes in your input assumptions | Review sensitivity/shadow prices where the model and decision warrant it |
How It Works
1. Share your problem
Tell us the real-world problem, the objective, and the constraints — plus any existing model or code
2. We identify the right formulation
We confirm whether this is linear, integer, mixed-integer, nonlinear, convex, or constraint-based, and formulate it accordingly
3. We solve it with an appropriate method
We choose and apply a solving approach suited to the actual structure of your problem, not a one-size-fits-all method
4. We verify the solution makes sense
We check the result against the real-world problem, not just mathematical correctness, to catch formulation errors
5. We explain the result clearly
You get a plain-English explanation of the solution and what it means, not just numbers out of a solver
Why Codersarts
Optimization problems fail in two different places — a wrong formulation, or the right formulation solved the wrong way — and diagnosing which one you're dealing with takes real experience. We work across linear, integer, mixed-integer, nonlinear, convex, and constraint optimization, for researchers formulating a novel problem, and teams trying to optimize a real operational process. We explain the reasoning behind the model and the solution, not just deliver an answer.
Turnaround Time
Well-defined problems with a clear objective and constraints are typically turned around within a few days. More open-ended or research-oriented problems, where the formulation itself needs development, are scoped with a clear timeline once we understand the problem. Research and launch deadlines are prioritized accordingly — let us know your timeline upfront.
FAQ
I don't know which type of optimization my problem is — can you help me figure that out?
Yes — this is one of the most common starting points. Describe the actual problem and we'll help identify the right category and formulation.
Do you work with a specific solver or programming language?
Yes — we work across common tools including Python (PuLP, SciPy, Pyomo), MATLAB, R, and solvers like CPLEX, Gurobi, and GLPK, depending on your needs.
Can you help if I already have a model but it's not solving correctly?
Yes — diagnosing why an existing model won't converge, returns an infeasible result, or gives an unexpected answer is a common request.
Is this for coursework/assignments, or only real business problems?
Both — we support academic coursework and research as well as real operational optimization problems.
Will you explain the solution, or just give me the answer?
We explain the result and the reasoning behind it — useful whether you need to understand it for a class, defend it to stakeholders, or build on it further.
Is our project kept confidential?
Yes. Your data, code, and results stay confidential, and an NDA is available on request.
Related Services
Working Through an Optimization Problem?
Whether it's research or a real operational challenge — get the formulation and the solution right.