Recently Fujiwara, Han and Mangasarian introduced a new constraint qualification which is a slight tightening of the well-known Mangasarian—Fromovitz constraint qualification. We show that this new qualification is a...
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Recently Fujiwara, Han and Mangasarian introduced a new constraint qualification which is a slight tightening of the well-known Mangasarian—Fromovitz constraint qualification. We show that this new qualification is a necessary and sufficient condition for the uniqueness of Kuhn—Tucker multipliers. We also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum.
This paper proposes a family of optimized transmitter and receiver FIR filters for orthogonal frequency division multiplex (OFDM) systems with offset QAM modulation using nonlinear-programming. Two objective Functions...
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This paper proposes a family of optimized transmitter and receiver FIR filters for orthogonal frequency division multiplex (OFDM) systems with offset QAM modulation using nonlinear-programming. Two objective Functions in the Frequency domain (considering both OFDM orthogonal condition and Nyquist condition), least square error (LSE) and minimizing maximal spectral side lobe (Mini-max), are used. The nonlinear programming is implemented with a modified sequential quadratic programming (SQP) algorithm, which guarantees a super-linear convergence. Resultant optimized FIR filters are given with their coefficients and spectra.
Peaking CO2 emissions and reaching carbon neutrality create a major role for hydrogen in the transportation field where decarbonization is difficult. Shanxi, as a microcosm of China in the systematic transformation of...
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Peaking CO2 emissions and reaching carbon neutrality create a major role for hydrogen in the transportation field where decarbonization is difficult. Shanxi, as a microcosm of China in the systematic transformation of energy end-use consumption, is selected to investigate the hydrogen energy development forecast for decarbonization in the transportation sector. Multi-supply-demand integrated scenario analysis with nonlinear programming (NLP) model is established to analyze hydrogen energy deployment in varied periods and regions under minimum environmental, energy and economic objectives, to obtain CO2 emission reduction potential. Results reveal that green hydrogen contributes most to low- carbon hydrogen development strategies. In high-hydrogen demand scenarios, carbon emission reduction potential is significantly higher under environmental objectives, esti- mated at 297.68 x 104-848.12 x 104 tons (2025-2035). The work provides a strategy to forecast hydrogen energy deployment for transportation decarbonization, being of vital significant guide for planning of hydrogen energy transportation in other regions. (c) 2022 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
There is much current interest in general equality constrained quadratic programming problems, both for their own sake and for their applicability to active set methods for nonlinear programming. In the former case, t...
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There is much current interest in general equality constrained quadratic programming problems, both for their own sake and for their applicability to active set methods for nonlinear programming. In the former case, typically, the issues are existence of solutions and their determination. In the latter instance, nonexistence of solutions gives rise to directions of infinite descent. Such directions may subsequently be used to determine a more desirable active set.
We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to ...
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We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.
General conditions are presented for the convergence of methods for solving conditional minimization problems. The conditions are necessary and sufficient for a certain class of sequential methods for unconditional mi...
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General conditions are presented for the convergence of methods for solving conditional minimization problems. The conditions are necessary and sufficient for a certain class of sequential methods for unconditional minimization. They are further generalized to problems of multicriterial optimization. The conditions have a clear geometric interpretation.
We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the S...
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We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new algorithmic framework that blends local search using the nonconvex POP into global descent using the convex SDP. In particular, we first design a globally convergent inexact projected gradient method (iPGM) for solving the SDP that serves as the backbone of our framework. We then accelerate iPGM by taking long, but safeguarded, rank-one steps generated by fast nonlinear programming algorithms. We prove that the new framework is still globally convergent for solving the SDP. To solve the iPGM subproblem of projecting a given point onto the feasible set of the SDP, we design a two-phase algorithm with phase one using a symmetric Gauss-Seidel based accelerated proximal gradient method (sGS-APG) to generate a good initial point, and phase two using a modified limited-memory BFGS (L-BFGS) method to obtain an accurate solution. We analyze the convergence for both phases and establish a novel global convergence result for the modified L-BFGS that does not require the objective function to be twice continuously differentiable. We conduct numerical experiments for solving second-order SDP relaxations arising from a diverse set of POPs. Our framework demonstrates state-of-the-art efficiency, scalability, and robustness in solving degenerate SDPs to high accuracy, even in the presence of millions of equality constraints.
We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmooth...
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We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmoothness of the objective in that a first-order trust-region or quadratic regularization method applied to it takes at most O(epsilon(-2)) function evaluations to reduce the size of a first-order criticality measure below epsilon. Specializing this result to the case when the composite objective is an exact penalty function allows us to consider the objective-and constraint-evaluation worst-case complexity of nonconvex equality-constrained optimization when the solution is computed using a first-order exact penalty method. We obtain that in the reasonable case when the penalty parameters are bounded, the complexity of reaching within epsilon of a KKT point is at most O(epsilon(-2)) problem evaluations, which is the same in order as the function-evaluation complexity of steepest-descent methods applied to unconstrained, nonconvex smooth optimization.
This paper is concerned with the Holder properties of optimal solutions of a nonlinear programming problem with perturbations in some fixed direction. The Holder property is used to obtain the directional derivative f...
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This paper is concerned with the Holder properties of optimal solutions of a nonlinear programming problem with perturbations in some fixed direction. The Holder property is used to obtain the directional derivative for the marginal function.
Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an ...
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Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an approximate electrical load distribution over a network of a prespecificed discretization. Together with partial information about existing substations, we determine the optimal placement of electrical substations to sustain such a load that minimizes the cost of capital and losses. This requires solving large-scale quadratic programs with discrete variables for which we present a novel penalization-smoothing scheme. The choice of locations allows one to determine the optimal flows in this network, as required by physical requirements which provide us with an approximation of the distribution network. Furthermore, the scheme allows for approximating systems in the presence of no-go areas, such as lakes and fields. We examine the performance of our algorithm on the solution of a set of location problems and observe that the scheme is capable of solving large-scale instances, well beyond the realm of existing mixed-integer nonlinear programming solvers. We conclude with a case study in which a stage-wise extension of this scheme is developed to reflect the temporal evolution of load. (C) 2010 Elsevier Ltd. All rights reserved.
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