# Tag Info

Accepted

### Is This Constraint Convex?

Arguments 3 and 4 are incorrect. The Right-Hand Side (RHS) is not convex. Even if it were, setting a nonlinear equality with either side non-affine is non-convex. As the final coup de grace, even if ...
• 11.3k
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### Trustful Nonlinear Programming

Local nonlinear optimization solvers, such as IPOPT, are not guaranteed to find a feasible point for problems that are feasible. That is certainly the case for problems with non-convex constraints, ...
• 11.3k
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• 23.3k
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### Linearizing the square root of two binary summations

For $j\in\{0,1,2\}$, introduce binary variable $w_j$ to indicate whether $x+y=j$, and then impose the following linear constraints: \begin{align} \sum_{j=0}^2 w_j &= 1 \\ \sum_{j=0}^2 j\cdot w_j &...
• 23.3k
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### Approximation methods for a mixed integer convex optimization problem

Mosek 9.x can natively solve mixed-integer exponential cone problems. Formulate the problem in YALMIP, specifying the binary variables as binvar, and Mosek as the solver. YALMIP will call Mosek to ...
• 11.3k

### Find the farthest point in hypercube to an exterior point

This answers a comment by the OP, to explain why the other answers are correct. It is due to the following standard result. A concave objective subject to compact convex constraints has a global ...
• 11.3k
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### how to implement an optimization function with polynomial in Gurobi (Java)

This can be handled by transforming this to a bilinear problem, i.e., a problem only involving products of no more than 2 variables at a time. This is accomplished by lifting the problem into a higher ...
• 11.3k
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### How to convexify log(convex) function?

You are maximizing a convex quadratic (the monotonic log is irrelevant) so the maximum is attained at the border, i.e. either $0$ or $\min(1,\sqrt{1-\text{constant}})$.
• 1,672
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### What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?

Disclaimer: One might want to look for a reformulation or a special structure to apply mathematical tools to find optimal in the feasible set. I am assuming you're already past the possibility that ...
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• 1,672