Convex optimization

About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.

Imputing a convex objective function

Abstract: We consider an optimizing process (or parametric optimization problem), i.e., an optimization problem that depends on some parameters. We present a method for imputing or estimating the objective function, based on observations of optimal or nearly optimal choices of the variable for several values of the parameter, and prior knowledge (or assumptions) about the objective. Applications include estimation of consumer utility functions from purchasing choices, estimation of value functions in control problems, given observations of an optimal (or just good) controller, and estimation of cost functions in a flow network.

New Regularized Algorithms for Transductive Learning

Abstract: We propose a new graph-based label propagation algorithm for transductive learning. Each example is associated with a vertex in an undirected graph and a weighted edge between two vertices represents similarity between the two corresponding example. We build on Adsorption, a recently proposed algorithm and analyze its properties. We then state our learning algorithm as a convex optimization problem over multi-label assignments and derive an efficient algorithm to solve this problem. We state the conditions under which our algorithm is guaranteed to converge. We provide experimental evidence on various real-world datasets demonstrating the effectiveness of our algorithm over other algorithms for such problems. We also show that our algorithm can be extended to incorporate additional prior information, and demonstrate it with classifying data where the labels are not mutually exclusive.

Solving Nonconvex Optimal Control Problems by Convex Optimization

Abstract: Motivated by aerospace applications, this paper presents a methodology to use second-order cone programming to solve nonconvex optimal control problems The nonconvexity arises from the presence of concave state inequality constraints and nonlinear terminal equality constraints The development relies on a solution paradigm, in which the concave inequality constraints are approximated by successive linearization Analysis is performed to establish the guaranteed satisfaction of the original inequality constraints, the existence of the successive solutions, and the equivalence of the solution of the original problem to the converged successive solution These results lead to a rigorous proof of the convergence of the successive solutions under appropriate conditions as well as nonconservativeness of the converged solution The nonlinear equality constraints are treated in a two-step procedure in which the constraints are first approximated by first-order expansions, then compensated by second-order correct

Radar waveform design in a spectrally crowded environment via nonconvex quadratic optimization

Abstract: Radar signal design in a spectrally crowded environment is a very challenging and topical problem due to the increasing demand for both military surveillance/remote-sensing capabilities and civilian wireless services. This paper deals with the synthesis of optimized radar waveforms ensuring spectral compatibility with the overlayed licensed electromagnetic radiators. A priori information, for instance, provided by a radio environmental map (REM), is exploited to force a spectral constraint on the radar waveform, which is thus the result of a constrained optimization process aimed at improving some radar performances (such as detection, sidelobes, resolution, tracking). The feasibility of the waveform optimization problem is extensively studied, and a solution technique leading to an optimal waveform is proposed. The procedure requires the relaxation of the original problem into a convex optimization problem and involves a polynomial computational complexity. At the analysis stage, the waveform performance is studied in terms of trade-off among the achievable signal to interference plus noise ratio (SINR), spectral shape, and the resulting autocorrelation function (ACF).

The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method

Abstract: This article is based on an idea proposed by C. W. Carroll for transforming a mathematical programming problem into a sequence of unconstrained minimization problems. It describes the theoretical validation of Carroll's proposal for the convex programming problem. A number of important new results are derived that were not originally envisaged: The method generates primal-feasible and dual-feasible points, the primal objective is monotonically decreased, and a subproblem of the original programming problem is solved with each unconstrained minimization. Briefly surveyed is computational experience with a newly developed algorithm that makes the technique competitive with known methodology. A subsequent article describing the computational algorithm is in preparation.