The Random-Facet algorithm is a randomized variant of the simplex method which is known to solve any linear program with n variables and m constraints using an expected number of pivot steps which is subexponential in both n and m. This is the theoretically fastest simplex algorithm known to date if m ≈ n; it provably beats most of the classical deterministic variants which require exp(Ω(n)) pi...

Lednicki and Wieczorkowski (2003) presented a method of stratification in subpopulations, based on the paper of Rivest (2002), which leads to obtain a fixed precision of a considered estimator for the particular subpopulations. They solved such a problem using a numerical simplex method of Nelder and Mead (1965). Because it is not the best solution of the question, (in a sense of an optimality ...

The problem of designing nonuniformly spaced arrays is formulated as one of constrained optimization in which the cost function is chosen to select the array with the minimum number of elements. The response of the array is controlled by a set of inequality point response constraints. It is shown that a suitable cost function for this problem is the I,, quasi-norm for 0 < p < 1 and that there e...

Simplex type algorithms perform successive pivoting operations (or iterations) in order to reach the optimal solution. The choice of the pivot element at each iteration is one of the most critical step in simplex type algorithms. The flexibility of the entering and leaving variable selection allows to develop various pivoting rules. In this paper, we have proposed some of the most well-known pi...

The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. Part I of this paper has developed a general and direct simplex algorithm for piecewise-linear programming, under convenient assumptions that guarantee a finite number of basic solutions, existence of basic feasible solutions, an...

This paper proposes a new real-value mutation operator and a hybrid real-coded genetic algorithm with quasi-simplex technique using this new mutation operator (RCGAQS). Compared with the classical GA (CGA), RCGAQS has the following distinguish features: (1) A new real-value mutation mechanism was used to increase the capability of global search (exploration); (2) The modified simplex technique,...

We prove that the simplex method with the highest gain/most-negative-reduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic MDP with n states and m actions, we prove the simplex method runs in O(nm log n) iterations if the discount factor is uniform and O(nm log n) iterations if e...

We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are polynomial in n. This answers a question of Frieze, Jerrum and Kannan Frieze et al. (1996). Our result can also be interpreted as efficiently learning the interse...

We consider the Nelder and Mead Simplex Method for the optimization of stochastic simulation models. Existing and new adaptive extensions of the Nelder and Mead simplex method designed to improve the accuracy and consistency of the observed best point are studied. We compare the performance of the extensions on a small microsimulation model, as well as on ve test functions. We found that gradua...