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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, ...
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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 ...
• 13.5k
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• 33.1k
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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 ...
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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 ...
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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 $\min(1,\sqrt{1-\text{constant}})$.
• 1,702
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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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How to maximize sum of cosine squared plus sum of sine squarred?

Allowing $\phi_k\in[-2\pi,2\pi]$ gives you enough freedom to achieve any angle $\theta_k$ as the common argument of $\cos$ and $\sin$. A geometric interpretation of your problem is to find a sequence ...
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• 1,702

Find an upper bound for an objective function

Yes, because $\log$ is monotonic, it preserves inequalities. The tightness depends on your other constraints.
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Endowment of an agent

Endowment is a term from economics. It is the (initial) amount of goods (or factors depending on the type of agent) an agent possesses. In models, this is an exogenous value (constant). Usually, there ...
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