Search · four archives
Search · four archives
17 papers · ranked by Valyu relevance
C. H. Jeffrey Pang
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs (QPs) and approximate projections arising from partially solving the QPs are…
C. H. Jeffrey Pang
The Set Intersection Problem (SIP) is the problem of finding a point in the intersection of convex sets. This problem is typically solved by the method of alternating projections. To accelerate the convergence, the idea of using Quadratic Programming (QP) to project a point onto the intersection of halfspaces generated…
C. H. Jeffrey Pang
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP) to project onto the intersection of supporting halfspaces generated earlier by…
Fahaar Mansoor Pirani, Fırdevs Ulus
There is an existing exact algorithm that solves DC programming problems if one component of the DC function is polyhedral convex [16]. Motivated by this, first, we consider two cutting-plane algorithms for generating an ǫ-polyhedral underestimator of a convex function g. The algorithms start with a polyhedral…
Daniel Ciripoi, Andreas Löhne, Benjamin Weißing
Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple…
Oliver Serang, Jérémie Bourdon
Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a…
Andreas H. Hamel, Andreas Löhne, Birgit Rudloff
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to…
Li Ge, Sanyang Liu
To globally solve a nonconvex quadratic programming problem, this paper presents an accelerating linearizing algorithm based on the framework of the branch-and-bound method. By utilizing a new linear relaxation approach, the initial quadratic programming problem is reduced to a sequence of linear relaxation programming…
John W. Pearson, Jacek Gondzio
Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and…
Olga Brezhneva, Agnieszka Prusińska, Alexey A. Tret’yakov, Ravi P. Agarwal
'Ravi P. Agarwal'] The paper describes an application of the p-regularity theory to Quadratic Programming (QP) and nonlinear equations with quadratic mappings. In the first part of the paper, a special structure of the nonlinear equation and a construction of the 2-factor operator are used to obtain an exact formula…
Fayyaz ul Amir Afsar Minhas
This paper analyzes the efficacy of applying one class classifiers (OCCs) to the problem of abnormal beat detection in ECG. It also proposes a novel OCC called Quadratic Programming Dissimilarity representation based Data Descriptor (QPDDD). A comparison of the proposed classification technique with existing…
Anthony J. Kearsley
The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here we consider the application of several optimization algorithms, both global and local, to this problem. The most promising…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Deniz Akdemir
Optimal subset selection is an important task that has numerous algorithms designed for it and has many application areas. STPGA contains a special genetic algorithm supplemented with a tabu memory property (that keeps track of previously tried solutions and their fitness for a number of iterations), and with a…
Kevin L. Keys, Hua Zhou, Kenneth Lange
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss…
James Renegar, Mutiara Sondjaja
for which the current iterate is 1, the vector of all ones. Letting d denote the Euclidean projection of the objective vector Ec onto the nullspace of the constraint matrix AE, step from 1 to 1 − 1 kdk d (a step of unit length). Finally, reverse the scaling to obtain ¯e := E 1 − 1 kdk d , and define this to be the…
Matúš Benko, Helmut Gfrerer
We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of ${\mathcal{Q}}$-stationarity (Benko and Gfrerer in Optimization 66(1):61-92, [5]). We…