There are $n$ students in a class, and they must be divided into, say, $k$ groups. Each student ranks the other students in order of preference of working together. Is there a wa …

I am trying to optimize a function of the following form: $L = \int_{t=0}^{T}(AR-x)dt$, where A is a system parameter i.e. I am trying to find the optimum x(t) that minimizes L o …

Operating in a $\mathbb{R}^N$ Euclidean space, I have an objective function defined as follows: $\phi(\vec{w}, b) = \frac{1}{2} \cdot \vec{w}^T \bullet \vec{w}$ In this particula …

When solving a MILP (mixed integer linear program) using a linear relaxation, the solver finds a feasible solution much faster if there is no objective function. The same problem w …

Just because a problem is NP-complete doesn't mean it can't be usually solved quickly. The best example of this is probably the traveling salesman problem, for which extraordinari …

I have a N-point metric space defined by the pairwise distance matrix. I want to encode these N points with binary strings, i.e. each point will be mapped to a vertex in a hypercub …

Consider a real symmetric matrix $A\in\mathbb{R}^{n \times n}$. The associated quadratic form $x^T A x$ is a convex function on all of $\mathbb{R}^n$ iff $A$ is positive semidefin …

I have the quadratic integer program over $\mathbb{Z}^n$ $\displaystyle\min_{z \in \mathbb{Z}^n} \Phi (z) = \frac{1}{2} z^T Q z - r^T z + s$ subject to $G z = h$, and $z_i \in {0 …

I'm interested generally in discrete optimization problems formulated as 0-1 integer programs; essentially, anything of the form $$\Phi = \max_{\mathbf{x} \in \left\{0,1\right\} ^N …

If a feasible solution to a linear programming is known, and the corresponding value of the objective function is close to the optimum, can we get a feasible solution to the dual p …

The real world version: I have a united value (e.i. 12in, 120V 1.414 kg*m/s) where the units are specified as the rational exponents of the 5 base units; m, s, kg, C and K. Additi …

This is a follow up to this question. I'm interested in discrete optimization problems formulated as 0-1 integer programs; essentially, anything of the form $$\Phi = \max_{\mathbf …

I know the interior point method works both for Linear Programming (LP) and semidefinite programming (SDP). My question is, can the other popular method for solving LP, namely the …

Is there an algorithm in literature to compute an efficient (pareto optimal) and envy free cake cutting when there are only n=2 players and a Mediator?

I am minimizing a highly non-linear function. If I know the global minimum is at most some value, is this information helpful to design a faster algorithm than random restart? If …