This paper presents a class of dual-primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the gen...
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This paper presents a class of dual-primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the general PPA to the equivalent variational inequality of the extended convex programming with linear constraints can result in easy proximal subproblems. In theory, the sequence generated by the general PPA may fail to converge since the proximal regularization matrix is asymmetric sometimes. So we construct descent directions derived from the solution obtained by the general PPA. Different step lengths and descent directions are chosen with the negligible additional computational load. The global convergence of the new algorithms is proved easily based on the fact that the sequences generated are Fejer monotone. Furthermore, we provide a simple proof for the O(1/t) convergence rate of these algorithms.
Aiming to address the hydrogen economy and system efficiency of a fuel cell hybrid electric vehicle, this paper proposes comparison research of battery size optimization and an energy management strategy. One approach...
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Aiming to address the hydrogen economy and system efficiency of a fuel cell hybrid electric vehicle, this paper proposes comparison research of battery size optimization and an energy management strategy. One approach is based on a bi-loop dynamic programming strategy, which selects the optimal one by initializing the battery parameters in the outer loop and performs energy distribution in the inner loop. The other approach is a framework based on convex programming, which can simultaneously design energy management strategies and optimize battery size. In the dynamic programming algorithm, the influence of the different discrete steps of state variables on the results is analysed, and a discrete step that can guarantee the accuracy of the algorithm and reduce computational time is selected. The results based on the above two algorithms and considering the transient response limitations of the fuel cell are analysed as well. Finally, two driving cycles are chosen to verify and compare the performance of the proposed methodology. Simulation results show that the dynamic programming-based energy management strategy and battery size provide more accurate results, and the transient response of the fuel cell has little effect on the optimization results of the battery size and energy management strategies. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m individual functions without coupled variables. Trea...
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We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m individual functions without coupled variables. Treating the functions in the objective separately, the new method belongs to the category of operator splitting methods. We show the global convergence and estimate a worst-case convergence rate for the new method, and then illustrate its numerical efficiency by some applications.
We introduce and analyze a natural geometric version of Renegar's condition number R for the homogeneous convex feasibility problem associated with a regular cone C subset of R-n. Let Gr(n,m) denote the Grassmann ...
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We introduce and analyze a natural geometric version of Renegar's condition number R for the homogeneous convex feasibility problem associated with a regular cone C subset of R-n. Let Gr(n,m) denote the Grassmann manifold of m-dimensional linear subspaces of R-n, and consider the projection distance d(p)(W-1,W-2) := parallel to Pi W-1 - Pi W-2 parallel to (spectral norm) between W-1,W-2 is an element of Gr(n,m), where Pi(Wi) denotes the orthogonal projection onto W-i. We call C (W) := max{d(p)(W,W')(-1) vertical bar W-' is an element of Sigma(m)} the Grassmann condition number of W is an element of Gr(n,m), where the set of ill-posed instances Sigma(m). Gr(n,m) is defined as the set of linear subspaces touching C. We show that if W = im(A(T)) for a matrix A is an element of R-mxn, then C(W) <= R(A) <= C (W) kappa(A), where kappa(A) = parallel to A parallel to parallel to A(dagger)parallel to denotes the matrix condition number. This extends work by Belloni and Freund in [ Math. Program. Ser. A, 119 (2009), pp. 95-107]. Furthermore, we show that C (W) can also be characterized in terms of the Riemannian distance metric on Gr(n,m). This differential geometric characterization of C (W) is the starting point of the sequel [D. Amelunxen and P. Burgisser, Probabilistic analysis of the Grassman condition number, preprint, http:***/abs/1112.2603, 2011] to this paper, where the first probabilistic analysis of Renegar's condition number for an arbitrary regular cone C is achieved.
In this paper, we consider general convex programming problems and give a sufficient condition for the equality of the infimum of the original problem and the supremum of its ordinary dual. This condition may be seen ...
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In this paper, we consider general convex programming problems and give a sufficient condition for the equality of the infimum of the original problem and the supremum of its ordinary dual. This condition may be seen as a continuity assumption on the constraint sets (i.e. On the sublevel sets of the constraint function) under linear perturbation. It allows us to generalize as well as treat previous results in a unified framework. Our main result is in fact based on a quite general constraint qualification result for quasiconvex programs involving a convex objective function proven in the setting of a real normed vector space.
作者：
STURM, JFZHANG, SStudent
Assistant Professor Department of Econometrics University of Groningen Groningen The Netherlands
In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and the m constraint functions are all k-harmonically convex in the feasible set, t...
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In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and the m constraint functions are all k-harmonically convex in the feasible set, then the number of iterations needed to find an is-an-element-of-optimal solution is bounded by a polynomial in m, k, and log(1/is-an-element-of). The method requires either the optimal objective value of the problem or an upper bound of the harmonic constant k as a working parameter. Moreover, we discuss the relation between the harmonic convexity condition used in this paper and some other convexity and smoothness conditions used in the literature.
This paper proposes a novel geometric programming based formulation to solve a gate-sizing and retiming problem in the context of circuit optimization. The gate-sizing aspect of the problem involves continuous variabl...
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This paper proposes a novel geometric programming based formulation to solve a gate-sizing and retiming problem in the context of circuit optimization. The gate-sizing aspect of the problem involves continuous variables while the retiming problem involves the placement of registers in the circuit and can be naturally modeled using discrete variables. Our formulation is solved using first-order convex programming. We show promising experimental results on industrial circuits. We also investigate formally the computational complexity of the problem. To our knowledge, this is the first effort that solves this problem in a single optimization framework.
To solve optimization problems in real-time and robustly, we propose a piecewise dynamic network for solving convex programming constrained by inequalities and linear equalities. The network is proposed based on the p...
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To solve optimization problems in real-time and robustly, we propose a piecewise dynamic network for solving convex programming constrained by inequalities and linear equalities. The network is proposed based on the penalty method and includes two stages. The network in the first stage is a zeroing dynamic network to solve an equation. It makes sure that for any initial point, the state of the network enters the linear equality constraint set within a fixed time. The optimal solution to this convex programming is obtained by the network in the second stage which is a gradient-type dynamic network. A lower bound of the penalty parameter is given to ensure the validity of the network, which makes up for the deficiency of the existing works. A suitable activation function is introduced to promote fixed-time convergence of the network and to improve its anti-interference capability. As a result, the proposed piecewise dynamic network is robust against additional interferences. Some tests are presented to show the effectiveness of our network.
We present branching-on-hyperplane methods for solving mixed integer linear and mixed integer convex programs. In particular, we formulate the problem of finding a good branching hyperplane using a novel concept of ad...
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We present branching-on-hyperplane methods for solving mixed integer linear and mixed integer convex programs. In particular, we formulate the problem of finding a good branching hyperplane using a novel concept of adjoint lattice. We also reformulate the problem of rounding a continuous solution to a mixed integer solution. A worst case complexity of a Lenstra-type algorithm is established using an approximate log-barrier center to obtain an ellipsoidal rounding of the feasible set. The results for the mixed integer convex programming also establish a complexity result for the mixed integer second order cone programming and mixed integer semidefinite programming feasibility problems as a special case. Our results motivate an alternative reformulation technique and a branching heuristic using a generalized (e.g., ellipsoidal) norm reduced basis available at the root node.
In this brief, we propose a sequential convex programming (SCP) framework for minimizing the terminal state dispersion of a stochastic dynamical system about a prescribed destination-an important property in high-risk...
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In this brief, we propose a sequential convex programming (SCP) framework for minimizing the terminal state dispersion of a stochastic dynamical system about a prescribed destination-an important property in high-risk contexts such as spacecraft landing. Our proposed approach seeks to minimize the conditional value-at-risk (CVaR) of the dispersion, thereby shifting the probability distribution away from the tails. This approach provides an optimization framework that is not overly conservative and can accurately capture more information about true distribution, compared with methods which consider only the expected value, or robust optimization methods. The main contribution of this brief is to present an approach that: 1) establishes an optimization problem with CVaR dispersion cost 2) approximated with one of the two novel surrogates which is then 3) solved using an efficient SCP algorithm. In 2), two approximation methods, a sampling approximation (SA) and a symmetric polytopic approximation (SPA), are introduced for transforming the stochastic objective function into a deterministic form. The accuracy of the SA increases with sample size at the cost of problem size and computation time. To overcome this, we introduce the SPA, which avoids sampling by using an alternative approximation and thus offers significant computational benefits. Monte Carlo simulations indicate that our proposed approaches minimize the CVaR of the dispersion successfully.
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