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Solves the problem, populating `problem.optval` with the optimal value,
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as well as the values of the variables (accessed by [`evaluate`](@ref))
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and constraint duals (accessed by `cons.dual`), where applicable.
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Optional keyword arguments:
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* `check_vexity` (default: `true`): emits a warning if the problem is not DCP
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* `verbose` (default: `true`): emits a warning if the problem was not solved optimally or `warmstart=true` but is not supported by the solver.
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* `warmstart` (default: `false`): whether the solver should start the optimization from a previous optimal value (according to the current value of the variables in the problem, which can be set by [`value!`](@ref) and accessed by [`evaluate`](@ref)).
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* `silent_solver`: whether the solver should be silent (and not emit output or logs) during the solution process.
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