How to prove the optimality of gurobi for MIQCP?
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Currently, I am utilizing the Gurobi optimizer to solve a Mixed-Integer Quadratic Convex Programming (MIQCP) problem. While the optimizer provides solutions, I am interested in understanding the global optimality and would like to explore accessible publications or general algorithms that can shed light on this aspect.
Could you please recommend any publications or resources that discuss techniques for proving global optimality in MIQCPs? Alternatively, if there are general algorithms that provide insights into Gurobi's approach for solving MIQCPs, that information would be highly valuable.
I appreciate your attention and assistance in advance. Thank you!
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MIQCP is a convex optimization problem with integer variables. All convex optimization and integer programming optimization theory still holds and a lot of the technique Gurobi's uses is directly inherited from MIP optimization.
For a general understanding of convex optimization and the theory behind it, I recommend reading the book Convex Optimization by Vandenberghe and Boyd.
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@Xiaojing Just to note, MIQCP is typically interpreted as Mixed-Integer Quadratically Constrained Program, and problems in that class are generally not convex. I'd avoid using this acronym for "Quadratic Convex Programming". If the problem has linear constraints and a convex quadratic objective then "convex MIQP" would be the preferred label.
- Riley
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Hi Riley Clement,
I appreciate your prompt response. I'd like to clarify that my specific interest lies in solving a Mixed-Integer Quadratically Constrained Program (MIQCP), which involves several non-convex quadratic constraints.
In light of this, I am curious to know if Gurobi can guarantee a global optimal solution for MIQCPs with non-convex quadratic constraints. Are there any theoretical literature or proofs available that provide insights into Gurobi's capability to address this class of problems?
Thank you for your time and expertise.
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Gurobi is a global optimizer so in theory given enough time and memory it will find a globally optimal solution, however the time and memory requirements for difficult problems could be impractical.
We recorded a webinar when we released v9 which introduced the ability to handle non-convex quadratic problems: Non-Convex Quadratic Optimization Webinar
In more recent times we recorded a "Tech Talk" on this subject: A Practical Tour Through Non-convex Optimization
- Riley
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