In this paper, we study the low-rank matrix minimization problem, where loss function is convex but nonsmooth and penalty term defined by cardinality function. We first introduce an exact continuous relaxation, that is, both problems have same minimizers optimal value. particular, a class of lifted stationary points relaxed problem show any local minimizer must be point. addition, derive lower ...

We show that the general two layer constrained via minimization problem and the three layer constrained via minimization problem for HVH topologies are NP-hard. A backtracking and a heuristic algorithm for the three layer HVH constrained via minimization problem are proposed. The backtracking algorithm can also be used for three layer non HVH problems. Experimental results indicate that our heu...

in this paper, optimal distributed control of the time-dependent navier-stokes equations is considered. the control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. a mixed numerical method involving a quasi-newton algorithm, a novel calculation of the gradients and an inhomogeneous navier-stokes solver, to find the opt...

this paper explores the flexile flow lines where setup times are sequence- dependent. the optimization criterion is the minimization of total weighted completion time. we propose an iterated greedy algorithm (iga) to tackle the problem. an experimental evaluation is conducted to evaluate the proposed algorithm and, then, the obtained results of iga are compared against those of some other exist...

in recent years, wavelet packet modulation ofdm (wpm-ofdm) signals have been introduced for radar applications. these signals have important properties such as inherent high range resolution and high resistance of radar system against jamming reception. this paper investigates the problem of designing these family of signals according to the following criteria: constrained maximization of the d...

Optimal Reactive Power Dispatch (ORPD) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. Due to the stochastic behavior of loads, the ORPD requires a probabilistic mathematical model. In this paper, Monte Carlo Simulation (MCS) is used for modeling of load uncertainties in the ORPD problem. The problem is formulated as a nonlinear constrained mul...

The break minimization problem is to find a home-away assignment that minimizes the number of breaks for a given schedule of a round-robin tournament. In a recent paper, Elf et al. conjectured that this minimization problem is solvable in polynomial time if the optimal value of a given instance is less than the number of teams of the instance. We prove their conjecture affirmatively by showing ...

The variational inequality problem is reduced to an optimization problem with a di erentiable objective function and simple bounds. Theoretical results are proved, that relate stationary points of the minimization problem to solutions of the variational inequality problem. Perturbations of the original problem are studied and an algorithm that uses the smooth minimization approach for solving m...

In this paper, the minimization of the maximum aggregate inventory of all products for the common cycle time approach to the scheduling problem of a multi-products single machine system is considered. In the case of non-zero set up time and limited resources, a simply and easy to apply rule has been obtained for this optimization problem. Using this rule, one can obtain the optimal production s...