The combination of bit-interleaved coded modulation and orthogonal frequency-division multiplexing (BICOFDM) forms a powerful coded modulation scheme for transmission over wideband channels. Recently, Moon and Cox [1]...
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The combination of bit-interleaved coded modulation and orthogonal frequency-division multiplexing (BICOFDM) forms a powerful coded modulation scheme for transmission over wideband channels. Recently, Moon and Cox [1] presented a new power allocation method to minimize the biterror rate (BER) of BIC-OFDM. It requires the solution of a convex optimization problem and is limited to (complex) binary transmission. Motivated by their work, in this letter we present an alternative power allocation method, which has the advantages of being a linear program and applicable to arbitrary signal constellations. Our approach relies on a BER approximation which becomes tight for asymptotically large signal-to-noise ratios. Simulative evidence shows that the proposed power allocation method achieves a performance very close to that from [1] for the case of quadrature phase-shift keying.
We present an algorithm, analogous to Karmarkar's algorithm, for the linear programming problem: maximize c T x subject to Ax ⩽ b , which works directly to the space of linear inequalities. The main new idea in th...
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We present an algorithm, analogous to Karmarkar's algorithm, for the linear programming problem: maximize c T x subject to Ax ⩽ b , which works directly to the space of linear inequalities. The main new idea in this algorithm is the simple construction of a projective transformation of the feasible region that maps the current iterate x to the analytic center of the transformed feasible region.
This research develops a linear programming (LP) model to assess various options for sugar and biofuel production from sugarcane and other feedstock in Hawaii. More specifically, the study focuses on finding optimal s...
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This research develops a linear programming (LP) model to assess various options for sugar and biofuel production from sugarcane and other feedstock in Hawaii. More specifically, the study focuses on finding optimal sugar and biomass feedstock that would maximize producer profits in the production of sugar, ethanol and electricity. Feedstock included in the model were sugarcane, banagrass, energy cane and sweet sorghum. Given available land resources for growing energy crops on the island of Maui, four land resource scenarios were considered. If available land resources were used in the production of sugarcane and energy crops with added utilization of non-prime lands, Hawaii's ethanol goal for year 2020 could be achieved while maintaining two-thirds of Hawaii's current sugar production. Crop yields and unit production costs are key factors in determining optimal quantities of feedstock in the optimization model tested in this study. Published by Elsevier Ltd.
Although parametric optimization with uncertainties on the objective function (OF) or on the so-called "right-hand-side" (RHS) of the constraints has been addressed successfully in recent papers, very little...
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Although parametric optimization with uncertainties on the objective function (OF) or on the so-called "right-hand-side" (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra. (C) 2013 Elsevier Ltd. All rights reserved.
This paper proposes two sets of rules, Rule G and Rule P, for controlling step lengths in a generic primal-dual interior point method for solving the linear programming problem in standard form and its dual. Theoretic...
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This paper proposes two sets of rules, Rule G and Rule P, for controlling step lengths in a generic primal-dual interior point method for solving the linear programming problem in standard form and its dual. Theoretically, Rule G ensures the global convergence, while Rule P, which is a special case of Rule G, ensures the O(nL) iteration polynomial-time computational complexity. Both rules depend only on the lengths of the steps from the current iterates in the primal and dual spaces to the respective boundaries of the primal and dual feasible regions. They rely neither on neighborhoods of the central trajectory nor on potential function. These rules allow large steps without performing any line search. Rule G is especially flexible enough for implementation in practically efficient primal-dual interior point algorithms.
This paper is concerned with the problem of following a trajectory from an infeasible starting point directly to an optimal solution of the linear programming problem. A class of trajectories for the problem is define...
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This paper is concerned with the problem of following a trajectory from an infeasible starting point directly to an optimal solution of the linear programming problem. A class of trajectories for the problem is defined, based on the notion of a beta-balanced solution to the problem. Given a prespecified positive balancing constant beta, an infeasible solution x is said to be beta-balanced if the optimal value gap is less than or equal to beta times the infeasibility gap. Mathematically, this can be written as c(T)x - z* less than or equal to beta xi(T)x, where the linear form xi(T)x is the Phase I objective function and z* is the optimal objective value of the linear program. The concept of a beta-balanced solution is used to define a class of trajectories from an infeasible point to an optimal solution of a given linear program. Each trajectory has the properly that all points on or near the trajectory (in a suitable metric) are beta-balanced. The main thrust of the paper is the development of an algorithm that traces a given beta-balanced trajectory from a starting point near the trajectory to an optimal solution to the given linear programming problem in polynomial time. More specifically, the algorithm allows for fixed improvement in the bound on the Phase I and the Phase II objectives in O(n) Newton steps.
In this paper, a disjunctive cutting-plane-based branch-and-cut algorithm is developed to solve the 0-1 mixed-integer convex nonlinear programming (MINLP) problems. In a branch-and-bound framework, the 0-1 MINLP probl...
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In this paper, a disjunctive cutting-plane-based branch-and-cut algorithm is developed to solve the 0-1 mixed-integer convex nonlinear programming (MINLP) problems. In a branch-and-bound framework, the 0-1 MINLP problem is approximated with a 0-1 mixed-integer linear program at each node, and then the lift-and-project technology is used to generate valid cuts to accelerate the branching process. The cut is produced by solving a linear program that is transformed from a projection problem, in terms of the disjunction on a free binary variable, and its dual solutions are applied to lift the cut to become valid throughout the enumeration tree. A strengthening process is derived to improve the coefficients of the cut by imposing integrality on the left free binary variables. Finally, the computational results on four test problems indicate that the added cutting planes can reduce the branching process greatly and show that the proposed algorithm is very promising for large-scale 0-1 MINLP problems, because a linear program is always computationally less expensive than a nonlinear program.
This paper presents the properties of the minimum mean cycle-canceling algorithm for solving linear programming models. Originally designed for solving network flow problems for which it runs in strongly polynomial ti...
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This paper presents the properties of the minimum mean cycle-canceling algorithm for solving linear programming models. Originally designed for solving network flow problems for which it runs in strongly polynomial time, most of its properties are preserved. This is at the price of adapting the fundamental decomposition theorem of a network flow solution together with various definitions: that of a cycle and the way to calculate its cost, the residual problem, and the improvement factor at the end of a phase. We also use the primal and dual necessary and sufficient optimality conditions stated on the residual problem for establishing the pricing step giving its name to the algorithm. It turns out that the successive solutions need not be basic, there are no degenerate pivots, and the improving directions are potentially interior in addition to those on edges. For solving an m x n linear program, it requires a pseudo-polynomial number O (n A) of so-called phases, where A depends on the number of rows and the coefficient matrix. (c) 2021 Elsevier B.V. All rights reserved.
A scheme for solving linear programming problems based on the use of auxiliary functions that implement feedback in the system of constraints imposed on the variables to be found and on the Lagrange multipliers is pro...
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A scheme for solving linear programming problems based on the use of auxiliary functions that implement feedback in the system of constraints imposed on the variables to be found and on the Lagrange multipliers is proposed. The validity of the proposed approach is proved.
A linear program may have several optimal solutions, but the one that is closest to any given vector is unique. In [18], a globally convergent path-following interior-point-like method was proposed to locate the optim...
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A linear program may have several optimal solutions, but the one that is closest to any given vector is unique. In [18], a globally convergent path-following interior-point-like method was proposed to locate the optimal solution of a linear program that is closest to the origin. The method was based on a special regularized central path. However, no local convergence result is known about that method. In this article, by using the analytical properties of a variant of the regularized central path, we present a high-order path-following method that is globally and locally superlinearly convergent under certain conditions. This method can find the projection of any given vector onto the optimal solution set of the linear program with respect to the 2-norm.
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