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I have an optimization problem with linear objective function. The constraints are in two different groups. The first set of constraints are linear while the second set is nonlinear. The nonlinear con …

I have a convex optimization problem that is essentially a linear objective function over some linear constraints and also a semidefinite matrix in the following form: $ M= \left[ …

Consider the following optimization problem: $Min\;\;\; CX$ $AX\geq b$ $x_ix_j= x_s x_t\;\;\; i\neq j \neq s\neq t$ $x_j\geq 0;$ Where $A$ is the adjacency matrix and $C$ is a constant vector. …

Consider the following optimization problem: Min$_{x}$ $\qquad \sum_{(i,j,t,s)\in I_r}||x_ix_j-x_tx_s||^2$ S.t.: $\qquad x\in \mathcal{C} ;$ where $x=(x_1,x_2,...x_n)$ and $\quad x_j\geq 0\;\; j …

Consider an instance of non-convexoptimization problem: It seems that this problem is NP-complete. How can I find a suitable reduction for this?

Consider the following optimization problem: \begin{align} \text{Min}_{i\neq j\neq s\neq t} |x_i x_j-x_sx_t|\\ s.t: Ax=b\\ x\geq 0; \end{align} This problem can be seen as an instance of non convex …

Consider the following optimization problem: $\text{max}_{p} \quad ||p||^2 \\ s.t: x\geq 0\\ p\in D$ where $D$ is a convex set. Is this problem $\mathcal{NP}$-hard?