Here, C denotes a column vector of cost coefficients, X a column vector of variables, A = [ai,j ] is a coefficient matrix, B is a column vector representing the bounds in the inequalities and the multiplication operation is matrix multiplication. Linear programs arise in a wide range of applications and can be solved efficiently. The classical simplex algorithm has been very successful in pract...

We present a new optimization-theoretic approach to analyzing Follow-the-Leader style algorithms, particularly in the setting where perturbations are used as a tool for regularization. We show that adding a strongly convex penalty function to the decision rule and adding stochastic perturbations to data correspond to deterministic and stochastic smoothing operations, respectively. We establish ...

optimization of cutting conditions is a non-linear optimization with constraint and it is very important to the increase of productivity and the reduction of costs. in recent years, several evolutionary and meta-heuristic optimization algorithms were introduced. the cuckoo optimization algorithm (coa) is one of several recent and powerful meta-heuristics which is inspired by the cuckoos and the...

optimization models have been used to support decision making in production planning for a long time. however, several of those models are deterministic and do not address the variability that is present in some of the data. robust optimization is a methodology which can deal with the uncertainty or variability in optimization problems by computing a solution which is feasible for all possible ...

in the process of milk production, the highest cost relates to animal feed. based on reports provided by the experts, around seventy percent of dairy livestock costs included feed costs. in order to minimize the total price of livestock feed, according to the limits of feed sources in each region or season, and also the transportation and maintenance costs and ultimately milk price reduction, o...

Now, let us consider the case ofK = Kb with b ∈ (1,∞). For v ∈ R andQ ⊆ [d], let vQ denote the 6 projection of v to those dimensions inQ. Then for any v ∈ R, and any w ∈ Kb withQ = {i : wi 6= 7 0}, we know by Hölder’s inequality that 〈w,v〉 = 〈wQ,vQ〉 ≥ −‖w‖b · ‖vQ‖a , for a = b/(b− 1). 8 Moreover, one can have 〈wQ,vQ〉 = −‖w‖b · ‖vQ‖a , when |wi| /‖w‖b = |vi|/‖v‖a and 9 wivi ≤ 0 for every i ∈ Q. ...

We propose an approach to linear optimization with recourse that does not involve a probabilistic description of the uncertainty, and allows the decision-maker to adjust the degree of robustness of the model while preserving its linear properties. We model random variables as uncertain parameters belonging to a polyhedral uncertainty set and minimize the sum of the first-stage costs and the wor...

A Mathematical Program with Linear Complementarity Constraints (MPLCC) is an optimization problem where a continuously differentiable function is minimized on a set defined by linear constraints and complementarity conditions on pairs of complementary variables. This problem finds many applications in several areas of science, engineering and economics and is also an important tool for the solu...

This paper proposes an algorithm for online linear optimization problem over permutations; the objective of the online algorithm is to find a permutation of {1, . . . , n} at each trial so as to minimize the “regret” for T trials. The regret of our algorithm is O(n √ T lnn) in expectation for any input sequence. A naive implementation requires more than exponential time. On the other hand, our ...