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A new graph parameter related to bounded rank positive semidefinite matrix completions
new graph parameter bounded rank positive semidefinite matrix completions Optimization and Control
2012/4/23
The Gram dimension $\gd(G)$ of a graph $G$ is the smallest integer $k\ge 1$ such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the off-diagonal positions c...
Minimum-Time Quantum Transport with Bounded Trap Velocity
Minimum-Time Quantum Transport Bounded Trap Velocity Optimization and Control
2011/8/30
Abstract: We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system wit...
Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree
p-Royden boundary p-harmonic boundary p-harmonic function
2011/1/20
Let p be a real number greater than one and let be a connected graph of bounded degree. We show that the p-Royden boundary of with the p-harmonic boundary removed is a F-set. We...
Let kr(n, δ) be the minimum number of r-cliques in graphs with n vertices and minimum degree δ. We evaluate kr(n, δ) for δ ≤ 4n/5 and some other cases. Moreover, we give a construction, which we conje...
Optimal investment with bounded VaR for power utility functions
Portfolio optimization Stochastic optimal control Risk constraints Value-at-Risk
2010/4/27
We consider the optimal investment problem for Black-Scholes type financial market with bounded VaR measure on the whole investment interval $[0,T]$. The explicit form for the optimal strategies is fo...
Optimal consumption and investment with bounded downside risk for power utility functions
Portfolio optimization Stochastic optimal control Risk constraints Value-at-Risk Expected Shortfall
2010/4/27
We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization prob...